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Can I compute with newforms OEIS A116418 Expansion of a newform level 18 weight 3 and character [3]?

asked 2011-12-13 02:43:03 -0500

joro gravatar image

updated 2015-01-14 04:43:27 -0500

FrédéricC gravatar image

Can I compute with newforms OEIS A116418 Expansion of a newform level 18 weight 3 and character [3]

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.

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answered 2013-12-11 05:56:45 -0500

John Cremona gravatar image

Here 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)
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Asked: 2011-12-13 02:43:03 -0500

Seen: 175 times

Last updated: Dec 11 '13