On newforms for Kohnen plus spaces

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}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 ?_k{\wp_k} of M _k+1/2(4M) onto M_k+1/2⁺(8M){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.