On Wed, Apr 15, 2009 at 11:34 AM, Steve Finch <[email protected]> wrote:
>
> Hi William & David,
>
> Thank you for your help! From:
>
> http://magma.maths.usyd.edu.au/magma/htmlhelp/text1447.htm#14693
>
> I see that Magma (to which I do not have access)
> can answer my first question with something like:
>
> Basis(CuspidalSubspace(HalfIntegralWeightForms(4,9/2)));
>
> and can answer my second question with something
> like:
>
> Dimension(HalfIntegralWeightForms(28,3/2));
>
> Might some kind Magma user please confirm?
You can do it using the magma_free command in Sage:
sage: magma_free('Dimension(HalfIntegralWeightForms(28,3/2))')
4
sage: magma_free('Basis(CuspidalSubspace(HalfIntegralWeightForms(4,9/2)))')
[
q - 6*q^2 + 12*q^3 - 8*q^4 + 12*q^6 - 48*q^7 + 48*q^8 - 15*q^9 +
60*q^10 - 12*q^11 + O(q^12)
]
That command uses this webpage, which I created a long time ago to
give people easy
access to Magma:
http://magma.maths.usyd.edu.au/calc/
> And,
> from your replies, I infer that the underlying Magma
> code is unfortunately not available for Sage development?
Evidently not, though ironically I wrote the first version of it...
> David, what I really want is a printout of:
>
> Dimension(HalfIntegralWeightForms(n,3/2));
>
> for all n=4,8,12, ..., 1000. Hence I will be studying
> your algorithm carefully! If you see a way to do this
> swiftly, please write back. Much appreciation,
This will give you the output in 3 seconds:
magma_free('[[2*n,Dimension(HalfIntegralWeightForms(4*n,3/2))] : n in
[1..250]]')
William
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