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Computing the dimensions of spaces of modular & cusp forms

asked 2014-02-16 06:55:24 +0100

Peter Luschny gravatar image

updated 2014-02-16 06:57:24 +0100

In OEIS A159634 Steven Finch gave the following MAGMA snippet to compute the

coefficient for dimensions of spaces of modular & cusp forms of weight k/2, level 4n and trivial character, where k >= 5 is odd.

[[4*n, (Dimension(HalfIntegralWeightForms(4*n, 7/2)) + 
Dimension(CuspidalSubspace(HalfIntegralWeightForms(4*n, 5/2))))/2]:n in [1..70]];

How can this sequence be computed with Sage?

Note that this question is related to a conjecture of Enrique Pérez Herrero.

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answered 2014-02-18 05:48:07 +0100

It seems there are no function in Sage to compute this. You can use magma_free() command like this :
sage: magma_free('[[4*n, (Dimension(HalfIntegralWeightForms(4*n, 7/2)) + Dimension(CuspidalSubspace(HalfIntegralWeightForms(4*n, 5/2))))/2]:n in [1..70]]')

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On the one hand disappointing, on the other hand it emphasizes the importance of the conjecture.

Peter Luschny gravatar imagePeter Luschny ( 2014-02-20 08:24:14 +0100 )edit

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Asked: 2014-02-16 06:55:24 +0100

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Last updated: Feb 18 '14