Modular forms for \(\Gamma_0(N)\) over \(\QQ\)#
- class sage.modular.modform.ambient_g0.ModularFormsAmbient_g0_Q(level, weight)#
Bases:
ModularFormsAmbient
A space of modular forms for \(\Gamma_0(N)\) over \(\QQ\).
- cuspidal_submodule()#
Return the cuspidal submodule of this space of modular forms for \(\Gamma_0(N)\).
EXAMPLES:
sage: m = ModularForms(Gamma0(33),4) sage: s = m.cuspidal_submodule(); s Cuspidal subspace of dimension 10 of Modular Forms space of dimension 14 for Congruence Subgroup Gamma0(33) of weight 4 over Rational Field sage: type(s) <class 'sage.modular.modform.cuspidal_submodule.CuspidalSubmodule_g0_Q_with_category'>
- eisenstein_submodule()#
Return the Eisenstein submodule of this space of modular forms for \(\Gamma_0(N)\).
EXAMPLES:
sage: m = ModularForms(Gamma0(389),6) sage: m.eisenstein_submodule() Eisenstein subspace of dimension 2 of Modular Forms space of dimension 163 for Congruence Subgroup Gamma0(389) of weight 6 over Rational Field