# source:sage/modular/modform/ambient_g0.py@6083:f68f48ca4dac

Revision 6083:f68f48ca4dac, 3.0 KB checked in by William Stein <wstein@…>, 6 years ago (diff)

Fix coverage of more modular forms doctests.

Line
1r"""
2Modular Forms for \$\Gamma_0(N)\$ over \$\Q\$.
3
4TESTS:
5    sage: m = ModularForms(Gamma0(389),6)
7    True
8"""
9
10#########################################################################
11#       Copyright (C) 2006 William Stein <wstein@gmail.com>
12#
14#
16#########################################################################
17
18import sage.rings.all as rings
19
20import sage.modular.congroup as congroup
21
22import ambient
23import cuspidal_submodule
24import eisenstein_submodule
25import submodule
26
27class ModularFormsAmbient_g0_Q(ambient.ModularFormsAmbient):
28    """
29    A space of modular forms for Gamma_0(N) over QQ.
30    """
31    def __init__(self, level, weight):
32        r"""
33        Create a space of modular symbols for \$\Gamma_0(N)\$ of given
34        weight defined over \$\QQ\$.
35
36        EXAMPLES:
37            sage: m = ModularForms(Gamma0(11),4); m
38            Modular Forms space of dimension 4 for Congruence Subgroup Gamma0(11) of weight 4 over Rational Field
39            sage: type(m)
40            <class 'sage.modular.modform.ambient_g0.ModularFormsAmbient_g0_Q'>
41        """
42        ambient.ModularFormsAmbient.__init__(self, congroup.Gamma0(level), weight, rings.QQ)
43
44    ####################################################################
45    # Computation of Special Submodules
46    ####################################################################
47    def cuspidal_submodule(self):
48        r"""
49        Return the cuspidal submodule of this space of modular forms for \$\Gamma_0(N)\$.
50
51        EXAMPLES:
52            sage: m = ModularForms(Gamma0(33),4)
53            sage: s = m.cuspidal_submodule(); s
54            Cuspidal subspace of dimension 10 of Modular Forms space of dimension 14 for Congruence Subgroup Gamma0(33) of weight 4 over Rational Field
55            sage: type(s)
56            <class 'sage.modular.modform.cuspidal_submodule.CuspidalSubmodule_g0_Q'>
57        """
58        try:
59            return self.__cuspidal_submodule
60        except AttributeError:
61            if self.level() == 1:
62                self.__cuspidal_submodule = cuspidal_submodule.CuspidalSubmodule_level1_Q(self)
63            else:
64                self.__cuspidal_submodule = cuspidal_submodule.CuspidalSubmodule_g0_Q(self)
65        return self.__cuspidal_submodule
66
67    def eisenstein_submodule(self):
68        r"""
69        Return the Eisenstein submodule of this space of modular forms for \$\Gamma_0(N)\$.
70
71        EXAMPLES:
72            sage: m = ModularForms(Gamma0(389),6)
73            sage: m.eisenstein_submodule()
74            Eisenstein subspace of dimension 2 of Modular Forms space of dimension 163 for Congruence Subgroup Gamma0(389) of weight 6 over Rational Field
75        """
76        try:
77            return self.__eisenstein_submodule
78        except AttributeError:
79            self.__eisenstein_submodule = eisenstein_submodule.EisensteinSubmodule_g0_Q(self)
80        return self.__eisenstein_submodule
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