CoCalc -- Collaborative Calculation in the Cloud
Sharedsupport / 2015-03-17-232601-psage.sagewsOpen in CoCalc

Examples for support purposes...

import psage
from psage.modform.hilbert.sqrt5.hmf import F, HilbertModularForms
P = F.prime_above(31); Q = F.prime_above(11); R = F.prime_above(2)
H = HilbertModularForms(P*Q*R); H
Hilbert modular forms of dimension 32, level 2*a-38 (of norm 1364=2^2*11*31) over QQ(sqrt(5))
print H.hecke_matrix(3).str()
[0 1 1 0 2 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 2 0 0 0 0 1 0 0 0 0 0 0] [1 0 1 2 0 0 0 0 1 0 0 0 0 1 1 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0] [1 1 0 1 1 0 0 0 0 1 0 0 0 0 1 0 1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0] [0 2 1 0 1 1 0 0 0 0 0 0 2 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0] [2 0 1 1 0 0 1 0 0 0 0 0 0 0 0 2 0 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1] [0 0 0 0 1 0 2 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 1 1 0 0] [1 0 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 1] [0 1 0 0 0 0 0 0 2 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1] [0 0 1 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0] [0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0] [0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0] [0 0 0 2 0 0 0 1 0 0 0 0 0 0 0 1 1 2 0 0 0 0 1 0 0 0 0 0 1 0 1 0] [1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 2] [0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0] [0 0 0 0 2 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 2 0 0 0 0 0 1 0 1 0 1 0] [1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 1 0 0 0 1 0 1 0 0] [0 2 0 0 0 0 0 0 1 0 0 0 2 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1] [0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0] [0 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0] [2 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1 1] [0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 2 0 0 0] [0 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 2 0 0 0 0 1 1 1 0 0] [0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 0 1 1] [0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0] [1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 2 0 1 0 1 0 1] [0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1] [0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0] [0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 2 1 1 0 0 1 0 0 0 0 0] [0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 0 0 0 0 0] [0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0 0 0] [0 0 0 0 0 1 0 1 1 0 0 0 0 2 0 0 0 1 0 0 1 0 0 1 0 1 1 0 0 0 0 0]
H.hecke_matrix(3).charpoly().factor()
(x - 10) * (x - 5) * (x - 4) * (x - 1) * (x + 1) * (x + 2)^2 * (x + 5)^2 * (x - 2)^4 * x^6 * (x^2 - x - 8) * (x^2 + x - 4) * (x^3 + x^2 - 10*x - 8) * (x^3 + 2*x^2 - 24*x - 32)^2