# Modular Forms for $$\Gamma_0(N)$$ over $$\QQ$$¶

TESTS:

sage: m = ModularForms(Gamma0(389),6)
True

class sage.modular.modform.ambient_g0.ModularFormsAmbient_g0_Q(level, weight)

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


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Modular Forms for $$\Gamma_1(N)$$ and $$\Gamma_H(N)$$ over $$\QQ$$