| 1 | r""" |
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| 2 | Modular Forms for $\Gamma_0(N)$ over $\Q$. |
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| 3 | |
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| 4 | TESTS: |
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| 5 | sage: m = ModularForms(Gamma0(389),6) |
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| 6 | sage: loads(dumps(m)) == m |
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| 7 | True |
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| 8 | """ |
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| 9 | |
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| 10 | ######################################################################### |
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| 11 | # Copyright (C) 2006 William Stein <wstein@gmail.com> |
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| 12 | # |
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| 13 | # Distributed under the terms of the GNU General Public License (GPL) |
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| 14 | # |
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| 15 | # http://www.gnu.org/licenses/ |
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| 16 | ######################################################################### |
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| 17 | |
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| 18 | import sage.rings.all as rings |
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| 19 | |
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| 20 | import sage.modular.congroup as congroup |
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| 21 | |
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| 22 | import ambient |
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| 23 | import cuspidal_submodule |
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| 24 | import eisenstein_submodule |
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| 25 | import submodule |
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| 26 | |
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| 27 | class ModularFormsAmbient_g0_Q(ambient.ModularFormsAmbient): |
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| 28 | """ |
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| 29 | A space of modular forms for Gamma_0(N) over QQ. |
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| 30 | """ |
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| 31 | def __init__(self, level, weight): |
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| 32 | r""" |
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| 33 | Create a space of modular symbols for $\Gamma_0(N)$ of given |
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| 34 | weight defined over $\QQ$. |
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| 35 | |
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| 36 | EXAMPLES: |
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| 37 | sage: m = ModularForms(Gamma0(11),4); m |
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| 38 | Modular Forms space of dimension 4 for Congruence Subgroup Gamma0(11) of weight 4 over Rational Field |
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| 39 | sage: type(m) |
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| 40 | <class 'sage.modular.modform.ambient_g0.ModularFormsAmbient_g0_Q'> |
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| 41 | """ |
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| 42 | ambient.ModularFormsAmbient.__init__(self, congroup.Gamma0(level), weight, rings.QQ) |
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| 43 | |
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| 44 | #################################################################### |
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| 45 | # Computation of Special Submodules |
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| 46 | #################################################################### |
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| 47 | def cuspidal_submodule(self): |
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| 48 | r""" |
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| 49 | Return the cuspidal submodule of this space of modular forms for $\Gamma_0(N)$. |
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| 50 | |
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| 51 | EXAMPLES: |
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| 52 | sage: m = ModularForms(Gamma0(33),4) |
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| 53 | sage: s = m.cuspidal_submodule(); s |
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| 54 | Cuspidal subspace of dimension 10 of Modular Forms space of dimension 14 for Congruence Subgroup Gamma0(33) of weight 4 over Rational Field |
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| 55 | sage: type(s) |
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| 56 | <class 'sage.modular.modform.cuspidal_submodule.CuspidalSubmodule_g0_Q'> |
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| 57 | """ |
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| 58 | try: |
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| 59 | return self.__cuspidal_submodule |
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| 60 | except AttributeError: |
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| 61 | if self.level() == 1: |
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| 62 | self.__cuspidal_submodule = cuspidal_submodule.CuspidalSubmodule_level1_Q(self) |
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| 63 | else: |
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| 64 | self.__cuspidal_submodule = cuspidal_submodule.CuspidalSubmodule_g0_Q(self) |
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| 65 | return self.__cuspidal_submodule |
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| 66 | |
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| 67 | def eisenstein_submodule(self): |
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| 68 | r""" |
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| 69 | Return the Eisenstein submodule of this space of modular forms for $\Gamma_0(N)$. |
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| 70 | |
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| 71 | EXAMPLES: |
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| 72 | sage: m = ModularForms(Gamma0(389),6) |
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| 73 | sage: m.eisenstein_submodule() |
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| 74 | 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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| 75 | """ |
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| 76 | try: |
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| 77 | return self.__eisenstein_submodule |
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| 78 | except AttributeError: |
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| 79 | self.__eisenstein_submodule = eisenstein_submodule.EisensteinSubmodule_g0_Q(self) |
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| 80 | return self.__eisenstein_submodule |
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