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 Oesterlè (see [Cohen and Oesterlé, 1977]).

Example: Dimension Formulas (ex-57206a)#

> 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

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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

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