Cusp forms on the exceptional group of type E7

Abstract

Let G be the connected reductive group of type E7,3 over ℚ and L be the corresponding symmetric domain in ℂ27. Let τ = G(ℤ) be the arithmetic subgroup de ned by Baily. In this paper, for any positive integer k ≥ 10, we will construct a (non-zero) holomorphic cusp form on L of weight 2k with respect to τ from a Hecke cusp form in S2k-8(SL2(ℤ)). We follow Ikeda's idea of using Siegel's Eisenstein series, their Fourier{Jacobi expansions, and the compatible family of Eisenstein series.