The dimension of the space Sk(Γ0(N)) of weight k
cusp forms for Γ0(N).
The dimension of the new subspace of the space
Sk(Γ0(N)) of weight k cusp forms for Γ0(N).
The dimension of the space Sk(Γ1(N)) of weight k
cusp forms for Γ1(N).
The dimension of the new subspace of the space
Sk(Γ1(N)) of weight k cusp forms for Γ1(N).
The dimension of the space Sk(Γ1(N))(ε)
of cusp forms of weight k and Dirichlet character eps.
The level N is the modulus of eps. The dimension is computed
using the formula of Cohen and Oesterlè (see
[CO77]).
> DimensionCuspFormsGamma0(11,2);
1
> DimensionCuspFormsGamma0(1,12);
1
> DimensionCuspFormsGamma0(5077,2);
422
> DimensionCuspFormsGamma1(5077,2);
1071460
> G := DirichletGroup(5*7);
> eps := G.1*G.2;
> IsOdd(eps);
true
> DimensionCuspForms(eps,2);
0
> DimensionCuspForms(eps,3);
6
The dimension of the space of cuspidal modular symbols
is twice the dimension of the space of cusp forms.
> Dimension(CuspidalSubspace(ModularSymbols(eps,3)));
12
V2.28, 13 July 2023