On newforms for Kohnen plus spaces

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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.

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