A larger GL <inf>2</inf> large sieve in the level aspect

Abstract

In this paper we study the orthogonality of Fourier coefficients of holomorphic cusp forms in the sense of large sieve inequality. We investigate the family of GL 2 cusp forms modular with respect to the congruence subgroups Γ 1(q), with additional averaging over the levels q ~ Q. We obtain the orthogonality in the range N ≪ Q 2-δ for any δ > 0, where N is the length of linear forms in the large sieve. © 2012 Versita Warsaw and Springer-Verlag Wien.