Sharedsupport / 2015-03-15-cubic-field.sagewsOpen in CoCalc
Authors: Harald Schilly, ℏal Snyder, William A. Stein
License: GNU General Public License v3.0
Description: Examples for support purposes.
for N in [24..100]: S = CuspForms(N,2) print N print S.newforms('a')
S = CuspForms(41,2) D = S.newforms('a') D
[q + a0*q^2 + (-1/2*a0^2 - a0 + 3/2)*q^3 + (a0^2 - 2)*q^4 + (-a0 - 1)*q^5 + O(q^6)]
f = D[0]
K = f.hecke_eigenvalue_field(); K
Number Field in a0 with defining polynomial x^3 + x^2 - 5*x - 1
K.signature()
(3, 0)
proof.number_field(False) %time U = CyclotomicField(29).unit_group()
CPU time: 0.62 s, Wall time: 0.63 s