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# Basis for modular forms of half-integral weigt.

Given a character $\chi$ and $k$ odd how can one compute a basis for the space of modular forms $M_\frac{k}{2}(\Gamma_0(4),\chi)$. By compute a basis I mean, finding the beginning of the Fourier expansions. I am looking for computer programs, which can do that for me.

I have heard of the package SAGE, which seems to do the job for integral weight modular forms. There is even the function http://www.sagemath.org/doc/reference/sage/modular/modform/half_integral.html but the examples all have q-expansions starting with q, so I guess this is not really a basis for the space of all modular forms but only cusp forms. MAGMA does not seem to include this functionality, either.

So, are there any packages which can do this? Since I have not found a package, I have some doubts that there is really an algorithm working in general. If there is no algorithm known to handle this, what methods are available in order to compute a basis "by hand"?

Thanks.