quadratic twists of p-adic L-function vanish approximately

[TimoKellerMath]

I'm computing quadratic twists of the p-adic L-function of the modular abelian surface J_0(23) with p = 11 split in the coefficient ring using the Pollack–Stevens overconvergent modular symbols algorithm. The p-adic L-function seems to be correct, however all quadratic twists I computed are 0 up to precision 4, which is fishy.

from sage.modular.pollack_stevens.space import ps_modsym_from_simple_modsym_space
from sage.modular.pollack_stevens.padic_lseries import pAdicLseries

Nps = [[23, 11, 0, -4]] #, [29, 7, 0], [39, 7, 1]]
# J_0(23) has an 11-torsion point over Q
# the trivial character is unramified and even, need unramified and odd
# hence twist by Q(-1) of discriminant -4

for Npi in Nps:
    N = Npi[0]
    A = ModularSymbols(N,2,1).cuspidal_submodule().new_subspace().decomposition()[Npi[2]]
    print("A =", A)
    p = Npi[1]
    print("p =", p)
    prec = 4
    phi = ps_modsym_from_simple_modsym_space(A)
    print("computed phi")
    ap = phi.Tq_eigenvalue(p,prec)
    print("a_p =", ap)
    c1,c2 = phi.completions(p,prec)
    phi1,psi1 = c1
    phi2,psi2 = c2
    
    print("1st p")
    if N % p == 0:
        phi1p = phi1.lift(p, M = prec)
    else:
        phi1p = phi1.p_stabilize_and_lift(p,ap = psi1(ap), M = prec)
    print("computed phi1p for a_p =", psi1(ap))
    for D in [-1,-4,-3,-7,-15,-19,-23,-27,-31]:
        L1 = pAdicLseries(phi1p, quadratic_twist = D)
        print(L1)
        print(D, L1.series(prec))

    print("2nd p")
    if N % p == 0:
        phi2p = phi2.lift(p, M = prec)
    else:
        phi2p = phi2.p_stabilize_and_lift(p,ap = psi2(ap), M = prec)
    print("computed phi2p for a_p =", psi2(ap))
    for D in [-1,-4,-3,-7,-15,-19,-23,-27,-31]:
        L2 = pAdicLseries(phi2p, quadratic_twist = D)
        print(L2)
        print(D, L2.series(prec))

    print("")

Here is the output (Sage from GitHub from yesterday) for the first prime lying above 11:

A = Modular Symbols subspace of dimension 2 of Modular Symbols space of dimension 3 for Gamma_0(23) of weight 2 with sign 1 over Rational Field
p = 11
computed phi
a_p = -2*alpha - 4
1st p
computed phi1p for a_p = 1 + 4*11 + 10*11^2 + 4*11^3 + O(11^4)
11-adic L-series of Modular symbol of level 253 with values in Space of 11-adic distributions with k=0 action and precision cap 6
-1 9*11^2 + O(11^3) + (2*11^2 + O(11^3))*T + O(11^2)*T^2 + O(11)*T^3 + O(T^4)
11-adic L-series of Modular symbol of level 253 with values in Space of 11-adic distributions with k=0 action and precision cap 6
-4 O(T^4)
11-adic L-series of Modular symbol of level 253 with values in Space of 11-adic distributions with k=0 action and precision cap 6
-3 O(T^4)
11-adic L-series of Modular symbol of level 253 with values in Space of 11-adic distributions with k=0 action and precision cap 6
-7 O(T^4)
11-adic L-series of Modular symbol of level 253 with values in Space of 11-adic distributions with k=0 action and precision cap 6
-15 O(T^4)
11-adic L-series of Modular symbol of level 253 with values in Space of 11-adic distributions with k=0 action and precision cap 6
-19 O(T^4)
11-adic L-series of Modular symbol of level 253 with values in Space of 11-adic distributions with k=0 action and precision cap 6
-23 O(T^4)
11-adic L-series of Modular symbol of level 253 with values in Space of 11-adic distributions with k=0 action and precision cap 6
-27 O(T^4)
11-adic L-series of Modular symbol of level 253 with values in Space of 11-adic distributions with k=0 action and precision cap 6
-31 O(T^4)

CC: @roed314

Component: modular forms

Keywords: p-adic L-functions, OMS, modular forms

Issue created by migration from https://trac.sagemath.org/ticket/34686