def _dim_new_eisenstein(self):
"""
Compute the dimension of the Eisenstein submodule.
EXAMPLES::
sage: m = ModularForms(Gamma0(11), 4)
sage: m._dim_new_eisenstein()
0
sage: m = ModularForms(Gamma0(11), 2)
sage: m._dim_new_eisenstein()
1
"""
try:
return self.__the_dim_new_eisenstein
except AttributeError:
if arithgroup.is_Gamma0(self.group()) and self.weight() == 2:
if rings.is_prime(self.level()):
d = 1
else:
d = 0
else:
E = self.eisenstein_series()
d = len([g for g in E if g.new_level() == self.level()])
self.__the_dim_new_eisenstein = d
return self.__the_dim_new_eisenstein
def _dim_new_eisenstein(self):
"""
Compute the dimension of the Eisenstein submodule.
EXAMPLES::
sage: m = ModularForms(Gamma0(11), 4)
sage: m._dim_new_eisenstein()
0
sage: m = ModularForms(Gamma0(11), 2)
sage: m._dim_new_eisenstein()
1
"""
try:
return self.__the_dim_new_eisenstein
except AttributeError:
if arithgroup.is_Gamma0(self.group()) and self.weight() == 2:
if rings.is_prime(self.level()):
d = 1
else:
d = 0
else:
E = self.eisenstein_series()
d = len([g for g in E if g.new_level() == self.level()])
self.__the_dim_new_eisenstein = d
return self.__the_dim_new_eisenstein
def _dim_new_eisenstein(self):
"""
Return the dimension of the new Eisenstein subspace, computed
by enumerating all Eisenstein series of the appropriate level.
EXAMPLES::
sage: m = ModularForms(DirichletGroup(36).0,5); m
Modular Forms space of dimension 28, character [-1, 1] and weight 5 over Rational Field
sage: m._dim_new_eisenstein()
2
sage: m._dim_eisenstein()
8
"""
try:
return self.__the_dim_new_eisenstein
except AttributeError:
if self.character().is_trivial() and self.weight() == 2:
if rings.is_prime(self.level()):
d = 1
else:
d = 0
else:
E = self.eisenstein_series()
d = len([g for g in E if g.new_level() == self.level()])
self.__the_dim_new_eisenstein = d
return self.__the_dim_new_eisenstein
def _dim_new_eisenstein(self):
"""
Return the dimension of the new Eisenstein subspace, computed
by enumerating all Eisenstein series of the appropriate level.
EXAMPLES::
sage: m = ModularForms(DirichletGroup(36).0,5); m
Modular Forms space of dimension 28, character [-1, 1] and weight 5 over Rational Field
sage: m._dim_new_eisenstein()
2
sage: m._dim_eisenstein()
8
"""
try:
return self.__the_dim_new_eisenstein
except AttributeError:
if self.character().is_trivial() and self.weight() == 2:
if rings.is_prime(self.level()):
d = 1
else:
d = 0
else:
E = self.eisenstein_series()
d = len([g for g in E if g.new_level() == self.level()])
self.__the_dim_new_eisenstein = d
return self.__the_dim_new_eisenstein