Denote by $\mathbb{F}_q$ the finite field with $q$ elements, and $\operatorname{SL}_n(\mathbb{F}_q)$ the special linear group in $n$ variables.

What is the minimum dimension of nontrivial real representations of $\operatorname{SL}_n(\mathbb{F}_q)$? What about for the general liner group $\operatorname{GL}_n(\mathbb{F}_q)$?