Bounds for the number of cohomological automorphic representations of $G{L}_3\mathrm{/}\mathbb{Q}$ in the weight aspect

We prove a power saving over the trivial bound for the number of cohomological cuspidal automorphic representations of fixed level and growing weight on $G{L}_3\mathrm{/}\mathbb{Q}$, by adapting the methods of our earlier paper on $G{L}_2$.