def _p_stabilize_parent_space(self, p, new_base_ring):
r"""
Return the space of Pollack-Stevens modular symbols of level
`p N`, with changed base ring. This is used internally when
constructing the `p`-stabilization of a modular symbol.
INPUT:
- ``p`` -- prime number
- ``new_base_ring`` -- the base ring of the result
OUTPUT:
The space of modular symbols of level `p N`, where `N` is the level
of this space.
EXAMPLES::
sage: D = OverconvergentDistributions(2, 7)
sage: M = PollackStevensModularSymbols(Gamma(13), coefficients=D)
sage: M._p_stabilize_parent_space(7, M.base_ring())
Space of overconvergent modular symbols for Congruence Subgroup
Gamma(91) with sign 0 and values in Space of 7-adic distributions
with k=2 action and precision cap 20
sage: D = OverconvergentDistributions(4, 17)
sage: M = PollackStevensModularSymbols(Gamma1(3), coefficients=D)
sage: M._p_stabilize_parent_space(17, Qp(17))
Space of overconvergent modular symbols for Congruence
Subgroup Gamma1(51) with sign 0 and values in Space of
17-adic distributions with k=4 action and precision cap 20
"""
N = self.level()
if N % p == 0:
raise ValueError("the level is not prime to p")
from sage.modular.arithgroup.all import (Gamma, is_Gamma, Gamma0,
is_Gamma0, Gamma1, is_Gamma1)
G = self.group()
if is_Gamma0(G):
G = Gamma0(N * p)
elif is_Gamma1(G):
G = Gamma1(N * p)
elif is_Gamma(G):
G = Gamma(N * p)
else:
raise NotImplementedError
return PollackStevensModularSymbols(
G,
coefficients=self.coefficient_module().change_ring(new_base_ring),
sign=self.sign())
def _p_stabilize_parent_space(self, p, new_base_ring):
r"""
Return the space of Pollack-Stevens modular symbols of level
`p N`, with changed base ring. This is used internally when
constructing the `p`-stabilization of a modular symbol.
INPUT:
- ``p`` -- prime number
- ``new_base_ring`` -- the base ring of the result
OUTPUT:
The space of modular symbols of level `p N`, where `N` is the level
of this space.
EXAMPLES::
sage: D = OverconvergentDistributions(2, 7)
sage: M = PollackStevensModularSymbols(Gamma(13), coefficients=D)
sage: M._p_stabilize_parent_space(7, M.base_ring())
Space of overconvergent modular symbols for Congruence Subgroup
Gamma(91) with sign 0 and values in Space of 7-adic distributions
with k=2 action and precision cap 20
sage: D = OverconvergentDistributions(4, 17)
sage: M = PollackStevensModularSymbols(Gamma1(3), coefficients=D)
sage: M._p_stabilize_parent_space(17, Qp(17))
Space of overconvergent modular symbols for Congruence
Subgroup Gamma1(51) with sign 0 and values in Space of
17-adic distributions with k=4 action and precision cap 20
"""
N = self.level()
if N % p == 0:
raise ValueError("the level is not prime to p")
from sage.modular.arithgroup.all import (Gamma, is_Gamma, Gamma0,
is_Gamma0, Gamma1, is_Gamma1)
G = self.group()
if is_Gamma0(G):
G = Gamma0(N * p)
elif is_Gamma1(G):
G = Gamma1(N * p)
elif is_Gamma(G):
G = Gamma(N * p)
else:
raise NotImplementedError
return PollackStevensModularSymbols(G, coefficients=self.coefficient_module().change_ring(new_base_ring), sign=self.sign())