I am looking for more-or-less explicit matrices for the $p^2$ dimensional Weil representation of $Sp(4,\mathbb{F}_p)$, suitable for computer implementation. Ideally, I would like the images of the generating transvections $\theta_i: \delta_j\rightarrow \delta_j-(\delta_j,\delta_i)\delta_i$ where $(\;,\;)$ is the corresponding form. I would be just as happy to have the irreducible $(p^2+1)/2$ dimensional part.
Are these matrices written down somewhere? Or implemented in GAP?
My literature and GAP manual search haven't turned up anything.
