Bounds for the multiplicities of cohomological automorphic forms on GL _2

摘要

We prove a power saving for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on 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.