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# Modular Forms over a Non-minimal Base Ring

class `sage.modular.modform.ambient_R.``ModularFormsAmbient_R`(M, base_ring)

  Bases: `sage.modular.modform.ambient.ModularFormsAmbient`

  Ambient space of modular forms over a ring other than QQ.

  EXAMPLES:

      sage: M = ModularForms(23,2,base_ring=GF(7)) ## indirect doctest
      sage: M
      Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(23) of weight 2 over Finite Field of size 7
      sage: M == loads(dumps(M))
      True

  `change_ring`(R)

    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)
        Traceback (most recent call last):
        ...
        ValueError: Space cannot be defined over Rational Field

  `cuspidal_submodule`()

    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'>

  `modular_symbols`(sign=0)

    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

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