One of the reasons for the popularity of modular forms in number theory is that they are highly computable objects. There is a variety of ways in which you can get your hands on explicit examples (see for instance William Stein's Modular forms: a computational approach or Lloyd Kilford's Modular forms: a classical and computational introduction). And, of course, you can (and probably should) use Sage to generate and play with such examples.

One of the reasons for the lesser popularity of various generalisations of modular forms is that they currently lack good computational infrastructure. The good news is that this is a fairly active field of research. Thinking specifically of Siegel modular forms, there are rumours of an upcoming paper (and code) by Raum-Ryan-Skoruppa-Tornaría. While we wait for this, there is a recent preprint by Martin Raum with the descriptive title Efficiently generated spaces of classical Siegel modular forms and the Böcherer conjecture. More precisely, its algorithmic focus is on genus 2, level 1, scalar-valued Siegel modular forms of high weight and with rational coefficients, and he conjectures the existence of a simple, nice-looking basis for these vector spaces (which we are encouraged to think of as an analogue of the Victor Miller basis for classical modular forms). He checked the conjecture computationally up to weight 172 (which is quite impressive) by using Sage.

This is excellent news, since the Victor Miller basis is a particularly efficient method for computing with classical modular forms, and it is wonderful to have this in the Siegel context. He shows off some of the power of this approach with a few interesting applications.