Re: ModularForms() error?

[William Stein]

On Thu, Jun 19, 2014 at 9:09 AM, Michael Somos
<so...@grail.cba.csuohio.edu> wrote:
> William Stein,
>
> Hello, I am Michael Somos. I have been using Sage
> for several years now, usually through a Virtual
> appliance on A Windows PC. Recently, I have been
> using sagecell.sagemath.org and today I have just
> created a SageMathCloud account. I am interested
> in modular forms. My problem is with the command
>
> ModularForms(Gamma1(29),1).basis()
>
> and I get a few lines of Traceback information
> about KeyError: 'text/plain' which seems not to
> be clear what caused it. I know that the space
> involved has "(unknown)" dimension and this is
> probably the cause of the problem. I get the
> same results using sagecell *and* SageMathCloud.
> However, when running Sage 6.2 from a bash command
> line the same command input gives an error message
>
> NotImplementedError: Computation of dimensions of weight 1 cusp forms not
> implemented in general
>
> which is more informative, but, still, I didn't
> ask for cusp forms.

ModularForms(Gamma1(29),1) = Eisenstein series + Cusp forms,

so you did indirectly ask for cusp forms.

> My main question is why the
> different error messages? Is there something very
> different with the "cloud" versus native? Shalom,
> Michael

Type

version()

into each version of Sage you're using. If the output is different,
then they are different versions of sage, and hence behave
differently. I have no idea why in this case the error messages
might be different.

There is no known efficient algorithm to compute spaces of weight 1
modular forms in general. There are very slow complicated algorithms
that do work in some cases, which are NOT implemented in Sage in
general. See, e.g., Springer Lecture Notes in Math 1585, which is
all about one such algorithm.

-- William

>
> --
> PUBLIC: Cleveland State University at http://cis.csuohio.edu/~somos/
> Dedekind eta product identities at http://eta.math.georgetown.edu/



--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org