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arXiv · 1801.10074

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

Yongquan Hu
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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.

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Yongquan Hu. 2018-01-30. Multiplicities of cohomological automorphic forms on $\mathrm{GL}_2$ and mod $p$ representations of $\mathrm{GL}_2(\mathbb{Q}_p)$. https://arxiv.org/abs/1801.10074

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