Dimension Formulas

DimensionCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt

The dimension of the space S_k(Gamma_0(N)) of weight k cusp forms for Gamma_0(N).

DimensionNewCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt

The dimension of the new subspace of the space S_k(Gamma_0(N)) of weight k cusp forms for Gamma_0(N).

DimensionCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt

The dimension of the space S_k(Gamma_1(N)) of weight k cusp forms for Gamma_1(N).

DimensionNewCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt

The dimension of the new subspace of the space S_k(Gamma_1(N)) of weight k cusp forms for Gamma_1(N).

DimensionCuspForms(eps, k) : GrpDrchElt, RngIntElt -> RngIntElt

The dimension of the space S_k(Gamma_1(N))(varepsilon) 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 Oesterl`e (see [CO77]).

Example ModSym_DimensionFormulas (H94E28)

> 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

> Dimension(CuspidalSubspace(ModularSymbols(eps,3)));  
12