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.

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Correspondence to Shunsuke Yamana.

Additional information

S. Yamana thanks Prof. Ikeda for useful discussion, and he is supported by JSPS Research Fellowships for Young Scientists.

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Ueda, M., Yamana, S. On newforms for Kohnen plus spaces. Math. Z. 264, 1 (2010). https://doi.org/10.1007/s00209-008-0449-8

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Keywords

  • Forms of half-integral weight
  • Newforms
  • Shimura correspondence
  • Kohnen plus space

Mathematics Subject Classification (2000)

  • 11F37