Multiplicities of cohomological automorphic forms on ${\mathrm{GL}}_2$ and mod $p$ representations of ${\mathrm{GL}}_2({\mathbb{Q}}_p)$

Abstract

We prove a new upper bound for the dimension of the space of cohomological automorphic forms of fixed level and growing parallel weight on ${\mathrm{GL}}_2$ over a number field which is not totally real, improving the one obtained by Marshall. The main tool of the proof is the mod $p$ representation theory of ${\mathrm{GL}}_2({\mathbb{Q}}_p)$ as started by Barthel-Livne and Breuil, and developed by Paskunas.

Final version

References in corpus (2)

• On the Breuil-Mézard conjecture
• Coefficient systems and supersingular representations of $G{L}_2(F)$

Cited by in corpus (1)

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