Newforms on Gamma_0(l) of Haupttypus
|Table 1: Range of the Modi data base|
|weight k||level l||range of a_f(n)|
|2||l ≤ 1000||n ≤ 100|
|4||l ≤ 200||n ≤ 100|
|6||l ≤ 120||n ≤ 100|
|8||l ≤ 60||n ≤ 100|
|10||l ≤ 40||n ≤ 100|
|12||l ≤ 30||n ≤ 100|
Currently the Modi data base contains the Fourier coefficients a_f(n) of all newforms f = sum_n a_f(n) q^n of integral weight k and Haupttypus on Gamma0(l) within the range of Table 1. For the origin of the data see [Cohen-Skoruppa-Zagier].
The Hecke algebra, i.e. the algebra generated over the rational numbers by the Hecke operators T(n) ( all n) acting on the space of newforms splits over the rationals into a direct product of totally real number fields. Modi can be queried for equations defining these fields, their discriminant and their Galois group, and the action of the Atkin-Lehner operators W_p on the subspaces of newforms belonging to these fields. Galois groups and discriminants are computed for equations of degree up to 11.
Galois groups are denoted by a 3-component vector [n,s,k], where n is the order of the group, s is its signature, i.e. s = 1 or -1 accordingly as the group is a subgroup of the alternating group A_n or not, and where k is the numbering of the group among all transitive subgroups of S_n as given in [Butler-McKay].