Abstract
We estimate the growth of cuspidal cohomology of GL2(AQ). Quantitatively, we provide bounds on the total number of normalised eigenforms of Hecke operators which are obtained by automorphic induction from Hecke characters of imaginary quadratic fields grows as level structure varies. We further investigate how much of cuspidal cohomology of GL3(AQ) is obtained by symmetric square transfer from GL2(AQ) when the level structure corresponds to power of an odd prime.
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