ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 11 Dec 2013 05:56:45 -0600Can I compute with newforms OEIS A116418 Expansion of a newform level 18 weight 3 and character [3]?http://ask.sagemath.org/question/8543/can-i-compute-with-newforms-oeis-a116418-expansion-of-a-newform-level-18-weight-3-and-character-3/Can I compute with newforms [OEIS A116418 Expansion of a newform level 18 weight 3 and character [3]](http://oeis.org/A116418)
Read the documentation but couldn't find how to describe the newform.
Using pari and the generating function I can compute it, but am interested in the newform method.Tue, 13 Dec 2011 02:43:03 -0600http://ask.sagemath.org/question/8543/can-i-compute-with-newforms-oeis-a116418-expansion-of-a-newform-level-18-weight-3-and-character-3/Answer by John Cremona for <p>Can I compute with newforms <a href="http://oeis.org/A116418">OEIS A116418 Expansion of a newform level 18 weight 3 and character [3]</a></p>
<p>Read the documentation but couldn't find how to describe the newform.</p>
<p>Using pari and the generating function I can compute it, but am interested in the newform method.</p>
http://ask.sagemath.org/question/8543/can-i-compute-with-newforms-oeis-a116418-expansion-of-a-newform-level-18-weight-3-and-character-3/?answer=15792#post-id-15792Here is how to compute such a newform:
sage: D=DirichletGroup(18)
sage: chi=D[3]
sage: S=ModularSymbols(chi,3).cuspidal_subspace().new_submodule()
sage: S
Modular Symbols subspace of dimension 4 of Modular Symbols space of dimension 12 and level 18, weight 3, character [-1], sign 0, over Rational Field
sage: [f.coefficients() for f in S.q_expansion_basis(prec=50)]
[[1, -2, -4, 6, 8, 4, -16, -24, 7, 8, 44, 18, -34, -12, -40, 24, -33],
[1, -3, -2, 12, -4, -9, 6, -12, 8, 3, 4, 12, -16, 33, -24, -60]]
The first one looks like the same sequence. But note that this is only a list of the nonzero coefficients:
sage: S.q_expansion_basis()[0]
q - 2*q^4 - 4*q^7 + O(q^8)
Wed, 11 Dec 2013 05:56:45 -0600http://ask.sagemath.org/question/8543/can-i-compute-with-newforms-oeis-a116418-expansion-of-a-newform-level-18-weight-3-and-character-3/?answer=15792#post-id-15792