## Fourier coefficients $C(a,b,c)$ of the extremal Siegel modular form ## of weight 36 and degree 2 for $0\le b \le a \le c \le 16$ ## ## --- Nils Skoruppa, April 2, 2008 (0, 0, 0) 1 (0, 0, 1) 0 (0, 0, 2) 0 (0, 0, 3) 0 (0, 0, 4) 6218175600 (0, 0, 5) 15281788354560 (0, 0, 6) 9026867482214400 (0, 0, 7) 1989179450818560000 (0, 0, 8) 213006159759990870000 (0, 0, 9) 13144087517631410995200 (0, 0, 10) 525100718690287495741440 (0, 0, 11) 14756609779472604266496000 (0, 0, 12) 310160311536865273422120000 (0, 0, 13) 5108106498702230684344320000 (0, 0, 14) 68347693198345293752360140800 (0, 0, 15) 764604200349778385836033966080 (0, 0, 16) 7318835829467289011348969122800 (1, 0, 1) 0 (1, 0, 2) 0 (1, 0, 3) 0 (1, 0, 4) 0 (1, 0, 5) 0 (1, 0, 6) 0 (1, 0, 7) 0 (1, 0, 8) 0 (1, 0, 9) 0 (1, 0, 10) 0 (1, 0, 11) 0 (1, 0, 12) 0 (1, 0, 13) 0 (1, 0, 14) 0 (1, 0, 15) 0 (1, 0, 16) 0 (1, 1, 1) 0 (1, 1, 2) 0 (1, 1, 3) 0 (1, 1, 4) 0 (1, 1, 5) 0 (1, 1, 6) 0 (1, 1, 7) 0 (1, 1, 8) 0 (1, 1, 9) 0 (1, 1, 10) 0 (1, 1, 11) 0 (1, 1, 12) 0 (1, 1, 13) 0 (1, 1, 14) 0 (1, 1, 15) 0 (1, 1, 16) 0 (2, 0, 2) 0 (2, 0, 3) 0 (2, 0, 4) 0 (2, 0, 5) 0 (2, 0, 6) 0 (2, 0, 7) 0 (2, 0, 8) 0 (2, 0, 9) 0 (2, 0, 10) 0 (2, 0, 11) 0 (2, 0, 12) 0 (2, 0, 13) 0 (2, 0, 14) 0 (2, 0, 15) 0 (2, 0, 16) 0 (2, 1, 2) 0 (2, 1, 3) 0 (2, 1, 4) 0 (2, 1, 5) 0 (2, 1, 6) 0 (2, 1, 7) 0 (2, 1, 8) 0 (2, 1, 9) 0 (2, 1, 10) 0 (2, 1, 11) 0 (2, 1, 12) 0 (2, 1, 13) 0 (2, 1, 14) 0 (2, 1, 15) 0 (2, 1, 16) 0 (2, 2, 2) 0 (2, 2, 3) 0 (2, 2, 4) 0 (2, 2, 5) 0 (2, 2, 6) 0 (2, 2, 7) 0 (2, 2, 8) 0 (2, 2, 9) 0 (2, 2, 10) 0 (2, 2, 11) 0 (2, 2, 12) 0 (2, 2, 13) 0 (2, 2, 14) 0 (2, 2, 15) 0 (2, 2, 16) 0 (3, 0, 3) 0 (3, 0, 4) 0 (3, 0, 5) 0 (3, 0, 6) 0 (3, 0, 7) 0 (3, 0, 8) 0 (3, 0, 9) 0 (3, 0, 10) 0 (3, 0, 11) 0 (3, 0, 12) 0 (3, 0, 13) 0 (3, 0, 14) 0 (3, 0, 15) 0 (3, 0, 16) 0 (3, 1, 3) 0 (3, 1, 4) 0 (3, 1, 5) 0 (3, 1, 6) 0 (3, 1, 7) 0 (3, 1, 8) 0 (3, 1, 9) 0 (3, 1, 10) 0 (3, 1, 11) 0 (3, 1, 12) 0 (3, 1, 13) 0 (3, 1, 14) 0 (3, 1, 15) 0 (3, 1, 16) 0 (3, 2, 3) 0 (3, 2, 4) 0 (3, 2, 5) 0 (3, 2, 6) 0 (3, 2, 7) 0 (3, 2, 8) 0 (3, 2, 9) 0 (3, 2, 10) 0 (3, 2, 11) 0 (3, 2, 12) 0 (3, 2, 13) 0 (3, 2, 14) 0 (3, 2, 15) 0 (3, 2, 16) 0 (3, 3, 3) 0 (3, 3, 4) 0 (3, 3, 5) 0 (3, 3, 6) 0 (3, 3, 7) 0 (3, 3, 8) 0 (3, 3, 9) 0 (3, 3, 10) 0 (3, 3, 11) 0 (3, 3, 12) 0 (3, 3, 13) 0 (3, 3, 14) 0 (3, 3, 15) 0 (3, 3, 16) 0 (4, 0, 4) 16190007309976500000 (4, 0, 5) 35587892367937644134400 (4, 0, 6) 19189979764187983994880000 (4, 0, 7) 3915056372713121506590720000 (4, 0, 8) 392157246823373524554767160000 (4, 0, 9) 22815094036067116416672399360000 (4, 0, 10) 864680546649537932127442668748800 (4, 0, 11) 23168788561524072743828513095680000 (4, 0, 12) 466239084104452813560725090662800000 (4, 0, 13) 7377366220726664080020924996894720000 (4, 0, 14) 95120236015577454300377020472770560000 (4, 0, 15) 1028026064084035856350615335429695078400 (4, 0, 16) 9527853919064586407778282641903364660000 (4, 1, 4) 9403393767505920000 (4, 1, 5) 23058568193888747520000 (4, 1, 6) 13371537921627754384588800 (4, 1, 7) 2873154670495340827115520000 (4, 1, 8) 299188340573755120397844480000 (4, 1, 9) 17939468769750199152560701440000 (4, 1, 10) 696493513014670977176939397120000 (4, 1, 11) 19033951848157138297669295328460800 (4, 1, 12) 389374455519877019207039554682880000 (4, 1, 13) 6247312131233122877138412174704640000 (4, 1, 14) 81514348500021896423748459089756160000 (4, 1, 15) 890110387762317192963989409758576640000 (4, 1, 16) 8324391778641716207590043642201348505600 (4, 2, 4) 1746861226809753600 (4, 2, 5) 6064103973068144640000 (4, 2, 6) 4419743083762372853760000 (4, 2, 7) 1116441062097505300316160000 (4, 2, 8) 131148832949368737507164160000 (4, 2, 9) 8632438971469088319484054732800 (4, 2, 10) 361006423947901988366322401280000 (4, 2, 11) 10482085671382670454435470376960000 (4, 2, 12) 225508069054838350623678185226240000 (4, 2, 13) 3775348635399911350698169154273280000 (4, 2, 14) 51085632524792846138576775512064000000 (4, 2, 15) 575679002453209318669389414722764800000 (4, 2, 16) 5533946339373569191309590082744074240000 (4, 3, 4) 86800557853900800 (4, 3, 5) 579577105135042560000 (4, 3, 6) 642881821703077232640000 (4, 3, 7) 217570743363869145169920000 (4, 3, 8) 31701985227277175840440320000 (4, 3, 9) 2461678310035914530318843904000 (4, 3, 10) 117333214358276905496973803520000 (4, 3, 11) 3788214318123188037549781155840000 (4, 3, 12) 88977230205725498285753462292480000 (4, 3, 13) 1603789710361950550543171450306560000 (4, 3, 14) 23112299344685778585170970386890752000 (4, 3, 15) 274998036486851741375563911478640640000 (4, 3, 16) 2771795428257504989745127330743582720000 (4, 4, 4) 794682841680000 (4, 4, 5) 16139478725959680000 (4, 4, 6) 35589528015949703577600 (4, 4, 7) 19189944908338970787840000 (4, 4, 8) 3915056911344913288805760000 (4, 4, 9) 392157240486752540662087680000 (4, 4, 10) 22815094094890136546553446400000 (4, 4, 11) 864680546189636623162116263116800 (4, 4, 12) 23168788565137140187947557723760000 (4, 4, 13) 466239084067920994442770987745280000 (4, 4, 14) 7377366221182280085251197648343040000 (4, 4, 15) 95120236010015278002607476671447040000 (4, 4, 16) 1028026064143696893649285197841781990400 (5, 0, 5) 78227319459969746872565760 (5, 0, 6) 42182344017763539407496806400 (5, 0, 7) 8605858712004114955447173120000 (5, 0, 8) 862018202871523842344852520960000 (5, 0, 9) 50150868103570232637147127165747200 (5, 0, 10) 1900692584273048184820809905586831360 (5, 0, 11) 50928339695748099947658896449889894400 (5, 0, 12) 1024860768627576537867711831700930560000 (5, 0, 13) 16216515246425161434468481296480337920000 (5, 0, 14) 209088001239089711658369229893793952563200 (5, 0, 15) 2259749596692846886142750695272034908241920 (5, 0, 16) 20943597445542080946256771259106898378752000 (5, 1, 5) 55306051763530283089920000 (5, 1, 6) 31604424672630422433300480000 (5, 1, 7) 6720283423684407741288284160000 (5, 1, 8) 694349015686153814741996666880000 (5, 1, 9) 41381535137208257925255580876800000 (5, 1, 10) 1598851637361140515376237228851200000 (5, 1, 11) 43521012616482813334234835032473600000 (5, 1, 12) 887369735103131375281056676803379200000 (5, 1, 13) 14197729268731107346532701102292336640000 (5, 1, 14) 184808542803697736872194059200323256320000 (5, 1, 15) 2013877393902196517341414307718601113600000 (5, 1, 16) 18799902425497523325857137476023489003520000 (5, 2, 5) 19130045199622710312960000 (5, 2, 6) 13097196647018369459159040000 (5, 2, 7) 3165696818136911149345013760000 (5, 2, 8) 359894888324267444473630556160000 (5, 2, 9) 23097451748315181386839732224000000 (5, 2, 10) 946698069851284214453170140610560000 (5, 2, 11) 27041541470168597352753197497712640000 (5, 2, 12) 573906485009802403601434878277386240000 (5, 2, 13) 9498517626423701367267481125400780800000 (5, 2, 14) 127274195626955141362889888833870233600000 (5, 2, 15) 1422135773897012891366684246654032281600000 (5, 2, 16) 13570047881622807053736676477862966722560000 (5, 3, 5) 3021944061571985571840000 (5, 3, 6) 2864313130952119350067200000 (5, 3, 7) 869434121044992052439285760000 (5, 3, 8) 116971946480787907682050375680000 (5, 3, 9) 8545605446337861673639319961600000 (5, 3, 10) 388175570481909908246557084876800000 (5, 3, 11) 12053737723606713842160710933544960000 (5, 3, 12) 274151316675233910901810040375869440000 (5, 3, 13) 4809726936654591097371730340531404800000 (5, 3, 14) 67735690894541250511381571428293672960000 (5, 3, 15) 790105617807999834939053238931465175040000 (5, 3, 16) 7827272454574002299461131003245287833600000 (5, 4, 5) 190982927418045235200000 (5, 4, 6) 302710773995815627653120000 (5, 4, 7) 130745010496792388437278720000 (5, 4, 8) 22744846571841532888452218880000 (5, 4, 9) 2020643912046095915068411084800000 (5, 4, 10) 107051294592458781862063295692800000 (5, 4, 11) 3763724324932769324302180774379520000 (5, 4, 12) 94827360506497289553058472034385920000 (5, 4, 13) 1812700432676197364134766593690828800000 (5, 4, 14) 27460757103885182948706377363895091200000 (5, 4, 15) 341082754318422806460252398076525281280000 (5, 4, 16) 3568746208831719596442391943752298496000000 (5, 5, 5) 3827835160910742159360 (5, 5, 6) 13330387947163166362828800 (5, 5, 7) 9715215177241063839498240000 (5, 5, 8) 2454098859343547606018949120000 (5, 5, 9) 288284050204891191869070901248000 (5, 5, 10) 18975346264823410159043114182901760 (5, 5, 11) 793544199852182252847639032129126400 (5, 5, 12) 23041136503270479614423438897971200000 (5, 5, 13) 495699268575145410329877417484615680000 (5, 5, 14) 8298760950287606047401214877786465894400 (5, 5, 15) 112293590131346619814798826226504664350720 (5, 5, 16) 1265425497567376450326027762102723988684800 (6, 0, 6) 22745891992275479394422415360000 (6, 0, 7) 4640518142763251308494685470720000 (6, 0, 8) 464824167351261243186486200094720000 (6, 0, 9) 27042741590648678994154709172879360000 (6, 0, 10) 1024906254795525053583784682818928640000 (6, 0, 11) 27461975876266533908896232592868638720000 (6, 0, 12) 552633403608942347908110980627841761280000 (6, 0, 13) 8744395618527131906651737790230230466560000 (6, 0, 14) 112746060065595955998561294770414380523520000 (6, 0, 15) 1218519772714120131542147975788185156530995200 (6, 0, 16) 11293369689275537202488888470501042526023680000 (6, 1, 6) 17885055318915578430068490240000 (6, 1, 7) 3776717581561465231370405806080000 (6, 1, 8) 388192803316516278545596822978560000 (6, 1, 9) 23042159081041524286761790787498803200 (6, 1, 10) 887409118985702128951647074868264960000 (6, 1, 11) 24091820970390308364808903475594526720000 (6, 1, 12) 490141800360157054926567308647797227520000 (6, 1, 13) 7827619847681168556066404227639691182080000 (6, 1, 14) 101728384355877982313164797095500956224716800 (6, 1, 15) 1107018249226293189067682568564261023907840000 (6, 1, 16) 10321765931175126631139066843875579438694400000 (6, 2, 6) 8606255325483989890273561804800 (6, 2, 7) 2020733368347750554823300218880000 (6, 2, 8) 224823709561230095140321673379840000 (6, 2, 9) 14190036271498343676798531545333760000 (6, 2, 10) 573931956574195649878016584946810880000 (6, 2, 11) 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23098477206088988645061500190720000 (6, 4, 9) 1900776937297064716731320967050035200 (6, 4, 10) 94831569209854046941539134845132800000 (6, 4, 11) 3176722600640577324708360532352040960000 (6, 4, 12) 76917204819822516150457762548735467520000 (6, 4, 13) 1422198891690282999788835342334781030400000 (6, 4, 14) 20944526973867017881063213447817030637158400 (6, 4, 15) 253899925269354542170360506160619905351680000 (6, 4, 16) 2601034116070799441720919980921021027942400000 (6, 5, 6) 31605823771762218426040320000 (6, 5, 7) 17885025073684346957872496640000 (6, 5, 8) 3776718046761926553537991802880000 (6, 5, 9) 388192797923688675037942807265280000 (6, 5, 10) 23042159129660589466442719789134643200 (6, 5, 11) 887409118639855316815166139525365760000 (6, 5, 12) 24091820972329225412373573584228843520000 (6, 5, 13) 490141800351790557544105645232955064320000 (6, 5, 14) 7827619847706869108319754358738980700160000 (6, 5, 15) 101728384355838183027890995614588121173196800 (6, 5, 16) 1107018249226199228755739872791328838123520000 (6, 6, 6) 1113056605512231917322240000 (6, 6, 7) 1130308082465936241752801280000 (6, 6, 8) 359910865827027313159428587520000 (6, 6, 9) 50153093826908316306904446035558400 (6, 6, 10) 3763891370995926935325367096442880000 (6, 6, 11) 174641931443621327309890629198151680000 (6, 6, 12) 5517152155002760783685434243570728960000 (6, 6, 13) 127279844360307314705903655495570554880000 (6, 6, 14) 2259849889934169017926086903545797017600000 (6, 6, 15) 32151345799809858597669668600199622164480000 (6, 6, 16) 378338223711936857107878583100410986086400000 (7, 0, 7) 946738366790990895119897135677440000 (7, 0, 8) 94831408794418502410773575578091520000 (7, 0, 9) 5517142745542279922929139003243888640000 (7, 0, 10) 209096924926227200761026415312691527680000 (7, 0, 11) 5602673104579667332865842800934162268160000 (7, 0, 12) 112745867990803178120188580745678321745920000 (7, 0, 13) 1783993634269785222611130778700192077578240000 (7, 0, 14) 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