Bounds for the multiplicities of cohomological automorphic forms on $\mathrm{GL}_2$

Abstract

We prove a power saving for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on $\mathrm{GL}_2$ over any number field that is not totally real. Our proof involves the theory of $p$-adically completed cohomology developed by Calegari and Emerton and a bound for the growth of coinvariants in certain finitely generated noncommutative Iwasawa modules.

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Authors

Simon Marshall

Department of Mathematics
Northwestern University
2033 Sheridan Road
Evanston, IL 60208-2730