Unconditional bounds for the multiplicity of automorphic forms of cohomological type on GL2
Abstract
We prove an unconditional power saving for the dimension of the space of cohomological automorphic forms of fixed level and growing weight on GL2 over any number field which 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 non-commutative Iwasawa modules.
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