Open Access
September 2014 Modular forms of half-integral weights on SL(2,Z)
Yifan Yang
Nagoya Math. J. 215: 1-66 (September 2014). DOI: 10.1215/00277630-2684452


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 {η(24τ)rf(24τ):f(τ)Ms(1)} is isomorphic to Sr+2s1new(6,(8r),(12r))(12) as Hecke modules under the Shimura correspondence. Here Ms(1) denotes the space of modular forms of weight s on Γ0(1)=SL(2,Z), S2knew(6,ϵ2,ϵ3) is the space of newforms of weight 2k on Γ0(6) that are eigenfunctions with eigenvalues ϵ2 and ϵ3 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.


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Yifan Yang. "Modular forms of half-integral weights on SL(2,Z)." Nagoya Math. J. 215 1 - 66, September 2014.


Published: September 2014
First available in Project Euclid: 8 May 2014

zbMATH: 1303.11057
MathSciNet: MR3263525
Digital Object Identifier: 10.1215/00277630-2684452

Primary: 11F37
Secondary: 11F11

Rights: Copyright © 2014 Editorial Board, Nagoya Mathematical Journal

Vol.215 • September 2014
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