On the growth of cuspidal cohomology of GL(2) and GL(3)

Abstract

We estimate the growth of cuspidal cohomology of GL(2)(A(Q)) 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 GL(3)(A(Q)) is obtained by symmetric square transfer from GL(2)(A(Q)) when the level structure corresponds to power of an odd prime.