$\DeclareMathOperator\SL{SL}$Let $p$ be an odd prime. It is easy to show that $\SL_2(3)$ can be embedded into $\SL_2(p)$.

Now, let $n$ be an integer larger than $2$.

Question: In which circumstances, $\SL_n(3)$ can be embedded into $\SL_n(p)$?