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Dimension Formulas

DimensionCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt
The dimension of the space Sk0(N)) of weight k cusp forms for Γ0(N).
DimensionNewCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt
The dimension of the new subspace of the space Sk0(N)) of weight k cusp forms for Γ0(N).
DimensionCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt
The dimension of the space Sk1(N)) of weight k cusp forms for Γ1(N).
DimensionNewCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt
The dimension of the new subspace of the space Sk1(N)) of weight k cusp forms for Γ1(N).
DimensionCuspForms(eps, k) : GrpDrchElt, RngIntElt -> RngIntElt
The dimension of the space Sk1(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 [CO77]).

Example ModSym_DimensionFormulas (H133E28)

> 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    
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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013