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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!

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!