This is related to my previous question here.

Let me remind you what that question asked:

Let $\text{St}_n(\mathbb{F}_q)$ be the Steinberg module (over $\mathbb{C}$) for $\text{SL}_n(\mathbb{F}_q)$.

What is the irreducible decomposition of the restriction of $\text{St}_{2n}(\mathbb{F}_q)$ to the symplectic group $\text{Sp}_{2n}(\mathbb{F}_q)$?

I got no answer, so I assume that this is an open question. This brings me to my new question. Let's say I wanted to calculate this for some small examples, say, $n=2$ and $q \in \{2,3,5\}$. Can this be done on a computer? I've tried to figure out how to do it with Magma and GAP, but this does not seem easy to me (this might just be my ignorance). Thanks!