\frametitle {Magma?}\begin {block}{But Magma can compute Hilbert Modular Forms...}
Why not just use Magma, which already has Hilbert modular forms in it, due to the
great work of John Voight, Lassina Dembele, and Steve Donnelly?
\begin{lstlisting}
[wstein@eno ~]$ magma
Magma V2.16-13 Fri Nov 5 2010 18:09:32 on eno [Seed = 666889163]
Type ? for help. Type -D to quit.
> F := QuadraticField(5);
> time M := HilbertCuspForms(F, Factorization(Integers(F)*100019)[1][1]);
Time: 0.030
> time T5 := HeckeOperator(M, Factorization(Integers(F)*5)[1][1]);
Time: 235.730 # 4 minutes
\end{lstlisting}
The value in Magma's HMF's are that the implementation is {\em very} general.
But slow. And the above was just one Hecke operator. We'll need many, and
Magma gets {\em much} slower as the subscript of the Hecke operator grows.
{\dred A factor of 1000 in speed kind of matters.}
\end{block}