Bases: sage.modular.modform.ambient.ModularFormsAmbient
Return this modular forms space with the base ring changed to the ring R.
EXAMPLE:
sage: chi = DirichletGroup(109, CyclotomicField(3)).0
sage: M9 = ModularForms(chi, 2, base_ring = CyclotomicField(9))
sage: M9.change_ring(CyclotomicField(15))
Modular Forms space of dimension 10, character [zeta3 + 1] and weight 2 over Cyclotomic Field of order 15 and degree 8
sage: M9.change_ring(QQ)
...
ValueError: Space cannot be defined over Rational Field
Return the cuspidal subspace of this space.
EXAMPLE:
sage: C = CuspForms(7, 4, base_ring=CyclotomicField(5)) # indirect doctest
sage: type(C)
<class 'sage.modular.modform.cuspidal_submodule.CuspidalSubmodule_R_with_category'>
Return the space of modular symbols attached to this space, with the given sign (default 0).
TESTS:
sage: K.<i> = QuadraticField(-1)
sage: chi = DirichletGroup(5, base_ring = K).0
sage: L.<c> = K.extension(x^2 - 402*i)
sage: M = ModularForms(chi, 7, base_ring = L)
sage: symbs = M.modular_symbols()
sage: symbs.character() == chi
True
sage: symbs.base_ring() == L
True