# Bounds for the number of cohomological automorphic representations of $GL_3/\mathbb{Q}$ in the weight aspect

## TL;DR

This paper establishes a power-saving bound on the number of cohomological automorphic representations of $GL_3/Q$ with fixed level and increasing weight, advancing understanding of automorphic forms in higher rank groups.

## Contribution

It extends previous methods from $GL_2$ to $GL_3$, providing new bounds for automorphic representations in the weight aspect.

## Key findings

- Achieved a power-saving bound over the trivial estimate.
- Extended techniques from $GL_2$ to $GL_3$ automorphic forms.
- Improved understanding of the growth of automorphic representations with weight.

## Abstract

We prove a power saving over the trivial bound for the number of cohomological cuspidal automorphic representations of fixed level and growing weight on $GL_3/\mathbb{Q}$, by adapting the methods of our earlier paper on $GL_2$.