Abstract
In this paper, we prove that, for an integer with and and a nonnegative even integer , the set is isomorphic to as Hecke modules under the Shimura correspondence. Here denotes the space of modular forms of weight on , is the space of newforms of weight on that are eigenfunctions with eigenvalues and for Atkin–Lehner involutions and , respectively, and the notation means the twist by the quadratic character . There is also an analogous result for the cases .
Citation
Yifan Yang. "Modular forms of half-integral weights on ." Nagoya Math. J. 215 1 - 66, September 2014. https://doi.org/10.1215/00277630-2684452
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