The file icosahedral-forms.txt was submitted to me by Arnaud Jehanne
(University Bordeaux I) March 2007. This file contains 27 icosahedral
forms of weight 1 and real nebentyp which are, to my best knowledge
state of June 2008, not covered by the known theorem concerning  which
2-dimensional odd Galois representations are modular. The
format of the file icosahedral forms is as follows:

[space, space, ...]

space:
    [ weight, level, character, form, form, ..., form, 512]

weight:
    always equal to $1$.

level:
    the $l$ such that the form is a new form for $\Gamma_0(l)$.

character:
    the negative discriminant $D$ such that the Kronecker symbol
    $\big(\frac D*\big)$ is the nebentyp of the forms in this space.

form:
    [ name, matrix, [pol_5, pol_24], coefficients]

name:
    the forms in a given space are called "a", "b", ....

matrix:
    ???

pol_5:
    polynomial defining the fixed field of the kernel of the
    corresponding projective Galois representation given as
    list of the coefficients in ascending order.

pol_24:
    polynomial defining the fixed field of the kernel of the
    corresponding (proper) Galois representation given as
    list of the coefficients in ascending order.

coefficients:
    5000 x 5 matrix $M$ , such that the vector $M*(1, S, i, iS)^t$
    contains the first 5000 Fourier coefficients of the form in
    question. Here $S=(-1+sqrt(5))/2$ and $i = \sqrt{-1}$.

The number 512 is meaningless (it used to be magic number for a PARI/GP
program).

The levels and characters of the 18 spaces containing these 27 forms
are as follows:

No.	level	char.	n. of forms
-----------------------------------
1	1948	-487	1
2	2083	-2083	1
3	2336	-292	2
4	2707	-2707	1
5	2863	-2863	2
6	3004	-751	1
7	3203	-3203	1
8	3547	-3547	1
9	3548	-887	1
10	3587	-3587	2
11	3676	-919	1
12	3775	-151	2
13	3775	-755	2
14	3875	-31	2
15	3875	-155	2
16	4000	-4	2
17	4000	-20	2
18	4027	-4027	1

Copyright (C) 2007
	Arnaud Jehanne (Universit\'e Bordeaux I)
        Nils Skoruppa (University of Siegen)