def compute_elldash(p, N, k0, n):
r"""
Returns the "Sturm bound" for the space of modular forms of level
`\Gamma_0(N)` and weight `k_0 + n(p-1)`.
.. seealso::
:meth:`~sage.modular.modform.space.ModularFormsSpace.sturm_bound`
INPUT:
- ``p`` -- prime.
- ``N`` -- positive integer (level).
- ``k0``, ``n`` - non-negative integers not both zero.
OUTPUT:
- positive integer.
EXAMPLES::
sage: from sage.modular.overconvergent.hecke_series import compute_elldash
sage: compute_elldash(11,5,4,10)
53
"""
return ModularForms(N, k0 + n * (p - 1)).sturm_bound()
def low_weight_bases(N, p, m, NN, weightbound):
r"""
Returns a list of integral bases of modular forms of level N and (even)
weight at most ``weightbound``, as `q`-expansions modulo `(p^m,q^{NN})`.
These forms are obtained by reduction mod `p^m` from an integral basis in
Hermite normal form (so they are not necessarily in reduced row echelon
form mod `p^m`, but they are not far off).
INPUT:
- ``N`` -- positive integer (level).
- ``p`` -- prime.
- ``m``, ``NN`` -- positive integers.
- ``weightbound`` -- (even) positive integer.
OUTPUT:
- list of lists of `q`-expansions modulo `(p^m,q^{NN})`.
EXAMPLES::
sage: from sage.modular.overconvergent.hecke_series import low_weight_bases
sage: low_weight_bases(2,5,3,5,6)
[[1 + 24*q + 24*q^2 + 96*q^3 + 24*q^4 + O(q^5)],
[1 + 115*q^2 + 35*q^4 + O(q^5), q + 8*q^2 + 28*q^3 + 64*q^4 + O(q^5)],
[1 + 121*q^2 + 118*q^4 + O(q^5), q + 32*q^2 + 119*q^3 + 24*q^4 + O(q^5)]]
"""
generators = []
for k in xrange(2, weightbound + 2, 2):
b = ModularForms(N, k, base_ring=Zmod(p**m)).q_expansion_basis(prec=NN)
generators.append(list(b))
return generators
