ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 20 Feb 2014 08:24:14 +0100Computing the dimensions of spaces of modular & cusp formshttps://ask.sagemath.org/question/11043/computing-the-dimensions-of-spaces-of-modular-cusp-forms/In OEIS [A159634](http://oeis.org/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](http://math.stackexchange.com/q/677949/129098) of Enrique Pérez Herrero.
Sun, 16 Feb 2014 06:55:24 +0100https://ask.sagemath.org/question/11043/computing-the-dimensions-of-spaces-of-modular-cusp-forms/Answer by moroplogo for <p>In OEIS <a href="http://oeis.org/A159634">A159634</a> Steven Finch gave the following
MAGMA snippet to compute the </p>
<p><em>coefficient for dimensions of spaces of modular & cusp forms of weight k/2, level 4n and trivial character, where k >= 5 is odd.</em></p>
<pre><code>[[4*n, (Dimension(HalfIntegralWeightForms(4*n, 7/2)) +
Dimension(CuspidalSubspace(HalfIntegralWeightForms(4*n, 5/2))))/2]:n in [1..70]];
</code></pre>
<p><em>How can this sequence be computed with Sage?</em></p>
<p>Note that this question is related to a <a href="http://math.stackexchange.com/q/677949/129098">conjecture</a> of Enrique Pérez Herrero. </p>
https://ask.sagemath.org/question/11043/computing-the-dimensions-of-spaces-of-modular-cusp-forms/?answer=16064#post-id-16064It 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]]')`Tue, 18 Feb 2014 05:48:07 +0100https://ask.sagemath.org/question/11043/computing-the-dimensions-of-spaces-of-modular-cusp-forms/?answer=16064#post-id-16064Comment by Peter Luschny for <p>It seems there are no function in Sage to compute this.
You can use magma_free() command like this : <br/>
<code>sage: magma_free('[[4*n, (Dimension(HalfIntegralWeightForms(4*n, 7/2)) + Dimension(CuspidalSubspace(HalfIntegralWeightForms(4*n, 5/2))))/2]:n in [1..70]]')</code></p>
https://ask.sagemath.org/question/11043/computing-the-dimensions-of-spaces-of-modular-cusp-forms/?comment=16229#post-id-16229On the one hand disappointing, on the other hand it emphasizes the importance of the conjecture.Thu, 20 Feb 2014 08:24:14 +0100https://ask.sagemath.org/question/11043/computing-the-dimensions-of-spaces-of-modular-cusp-forms/?comment=16229#post-id-16229