On newforms for Kohnen plus spaces

Abstract

In this article, we investigate the plus space of level N, where 4−1 N is a square-free (not necessarily odd) integer. This is a generalization of Kohnen’s work. We define a Hecke isomorphism \({\wp_k}\) of M k+1/2(4M) onto \({M_{k+1/2}^+(8M)}\) for any odd positive integer M. The methods of the proof of the newform theory are this isomorphism, Waldspurger’s theorem, and the dimension identity.