Wednesday status reports
Ran first parallel SAGE tasks on Lonestar using autogeneration code.
Vastly sped up Sage at computing Hecke eigenvalues a_n on S_2(\Gamma_0(N)). Coding work will easily (but tediously) generalize to S_k(N,\varepsilon). E.g., for S_2(\Gamma_0(43)) is about 25 times faster than before, and (22 times faster than Magma, by the way).
> A := NewformDecomposition(CuspidalSubspace(ModularSymbols(43,2,1)))[2]; > time k := CompactSystemOfEigenvalues(A,10^4); Time: 152.740
In Sage (on sage.math) before:
sage: M = ModularSymbols(43,2,sign=1)[2]; M Modular Symbols subspace of dimension 2 of Modular Symbols space of dimension 4 for Gamma_0(43) of weight 2 with sign 1 over Rational Field sage: time w = M.system_of_eigenvalues(10^4) CPU times: user 160.42 s, sys: 1.98 s, total: 162.40 s Wall time: 162.36 s
In Sage now:
sage: M = ModularSymbols(43,2,sign=1)[2]; M Modular Symbols subspace of dimension 2 of Modular Symbols space of dimension 4 for Gamma_0(43) of weight 2 with sign 1 over Rational Field sage: time E,v = M.compact_system_of_eigenvalues(prime_range(10^4)) CPU time: 7.24 s, Wall time: 7.53 s
Should now be ready to run on our data.