Prime degree irreducible representations of simple algebraic groups and finite simple groups of Lie type

Let $r, p$ be primes and $k$ be a positive integer. We show that if $G$ is a subgroup of $SL_r(p^k)$ lying only in the non-geometric Aschbacher class $\mathscr{C}_9$, then $|G|$ is bounded above by a function of $r$ and $k$, independently of $p$. We also show that, up to conjugacy in $GL_r(p^k)$, th