Arithmetic Groups

In this talk, I will establish a sharp bound on the growth of cuspidal Bianchi modular forms. By the Eichler-Shimura isomorphism, we actually give a sharp bound of the second cohomology of a hyperbolic three manifold (Bianchi manifold) with local system arising from the representation $\sim ^{k} \otimes \overline \sim{^k}$ of $SL_2(C)$. I will explain how a p-adic algebraic method is used for deriving our result.