Higher level cusp forms on exceptional group of type E7

Abstract

By using new techniques with the degenerate Whittaker functions developed by Ikeda and Yamana, we construct a higher-level cusp form on GE7,3 (exceptional similitude group of type E7), called Ikeda type lift, from any Hecke cusp form whose corresponding automorphic representation has no supercuspidal local components. This generalizes our earlier results on level-1 forms. But there is a new phenomenon in higher levels; we can handle cusp forms with nontrivial central characters. We also compute the degree-133 adjoint L-function of the Ikeda type lift.