def __init__(self, group, weight, base_ring, character=None):
"""
Create an ambient space of modular forms.
EXAMPLES::
sage: m = ModularForms(Gamma1(20),20); m
Modular Forms space of dimension 238 for Congruence Subgroup Gamma1(20) of weight 20 over Rational Field
sage: m.is_ambient()
True
"""
if not arithgroup.is_CongruenceSubgroup(group):
raise TypeError, 'group (=%s) must be a congruence subgroup' % group
weight = rings.Integer(weight)
if character is None and arithgroup.is_Gamma0(group):
character = dirichlet.TrivialCharacter(group.level(), base_ring)
space.ModularFormsSpace.__init__(self, group, weight, character,
base_ring)
try:
d = self.dimension()
except NotImplementedError:
d = None
hecke.AmbientHeckeModule.__init__(self, base_ring, d, group.level(),
weight)
def __init__(self,
group = arithgroup.Gamma0(1),
weight = 2,
sign = 0,
base_ring = rings.QQ,
character = None):
"""
Space of boundary symbols for a congruence subgroup of SL_2(Z).
This class is an abstract base class, so only derived classes
should be instantiated.
INPUT:
- ``weight`` - int, the weight
- ``group`` - arithgroup.congroup_generic.CongruenceSubgroup, a congruence
subgroup.
- ``sign`` - int, either -1, 0, or 1
- ``base_ring`` - rings.Ring (defaults to the
rational numbers)
EXAMPLES::
sage: B = ModularSymbols(Gamma0(11),2).boundary_space()
sage: isinstance(B, sage.modular.modsym.boundary.BoundarySpace)
True
sage: B == loads(dumps(B))
True
"""
weight = int(weight)
if weight <= 1:
raise ArithmeticError("weight must be at least 2")
if not arithgroup.is_CongruenceSubgroup(group):
raise TypeError("group must be a congruence subgroup")
sign = int(sign)
if not isinstance(base_ring, rings.Ring) and rings.is_CommutativeRing(base_ring):
raise TypeError("base_ring must be a commutative ring")
if character is None and arithgroup.is_Gamma0(group):
character = dirichlet.TrivialCharacter(group.level(), base_ring)
(self.__group, self.__weight, self.__character,
self.__sign, self.__base_ring) = (group, weight,
character, sign, base_ring)
self._known_gens = []
self._known_gens_repr = []
self._is_zero = []
hecke.HeckeModule_generic.__init__(self, base_ring, group.level())
