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Modular forms of half-integral weights on SL(2, ℤ)

Published online by Cambridge University Press:  11 January 2016

Yifan Yang
Yifan Yang*
Affiliation:
Department of Applied Mathematics, National Chiao Tung University and National Center for Theoretical Sciences, Hsinchu 300, Taiwan, [email protected]
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Abstract

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In this paper, we prove that, for an integer r with (r, 6) = 1 and 0 < r < 24 and a nonnegative even integer s, the set

is isomorphic to

as Hecke modules under the Shimura correspondence. Here Ms(1) denotes the space of modular forms of weight is the space of newforms of weight 2k on Γ0 (6) that are eigenfunctions with eigenvalues €2 and €3 for Atkin-Lehner involutions W2 and W3, respectively, and the notation ⊕(12/.) means the twist by the quadratic character (12/-). There is also an analogous result for the cases (r, 6) = 3.

Keywords

11F3711F11
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 215 , September 2014 , pp. 1 - 66
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

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