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# Constructors for certain modular abelian varieties

AUTHORS:

- William Stein (2007-03)

`sage.modular.abvar.constructor.``AbelianVariety`(X)

  Create the abelian variety corresponding to the given defining data.

  INPUT:

  - `X` - an integer, string, newform, modsym space, congruence subgroup or tuple of congruence subgroups

  OUTPUT: a modular abelian variety

  EXAMPLES:

      sage: AbelianVariety(Gamma0(37))
      Abelian variety J0(37) of dimension 2
      sage: AbelianVariety('37a')
      Newform abelian subvariety 37a of dimension 1 of J0(37)
      sage: AbelianVariety(Newform('37a'))
      Newform abelian subvariety 37a of dimension 1 of J0(37)
      sage: AbelianVariety(ModularSymbols(37).cuspidal_submodule())
      Abelian variety J0(37) of dimension 2
      sage: AbelianVariety((Gamma0(37), Gamma0(11)))
      Abelian variety J0(37) x J0(11) of dimension 3
      sage: AbelianVariety(37)
      Abelian variety J0(37) of dimension 2
      sage: AbelianVariety([1,2,3])
      Traceback (most recent call last):
      ...
      TypeError: X must be an integer, string, newform, modsym space, congruence subgroup or tuple of congruence subgroups

`sage.modular.abvar.constructor.``J0`(N)

  Return the Jacobian \(J_0(N)\) of the modular curve \(X_0(N)\).

  EXAMPLES:

      sage: J0(389)
      Abelian variety J0(389) of dimension 32

  The result is cached:

      sage: J0(33) is J0(33)
      True

`sage.modular.abvar.constructor.``J1`(N)

  Return the Jacobian \(J_1(N)\) of the modular curve \(X_1(N)\).

  EXAMPLES:

      sage: J1(389)
      Abelian variety J1(389) of dimension 6112

`sage.modular.abvar.constructor.``JH`(N, H)

  Return the Jacobian \(J_H(N)\) of the modular curve \(X_H(N)\).

  EXAMPLES:

      sage: JH(389,[16])
      Abelian variety JH(389,[16]) of dimension 64

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