This is related to my previous question <a href="http://mathoverflow.net/questions/182027/restricting-the-steinberg-representation-of-sl-2n-over-a-finite-field-to-the">here</a>.

Let me remind you what that question asked:

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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 $\text{Sp}_{2n}(\mathbb{F}_q)$?

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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!