Nagoya Mathematical Journal

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

Yifan Yang

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Abstract

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.

Article information

Source
Nagoya Math. J., Volume 215 (2014), 1-66.

Dates
First available in Project Euclid: 8 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1399554604

Digital Object Identifier
doi:10.1215/00277630-2684452

Mathematical Reviews number (MathSciNet)
MR3263525

Zentralblatt MATH identifier
1303.11057

Subjects
Primary: 11F37: Forms of half-integer weight; nonholomorphic modular forms
Secondary: 11F11: Holomorphic modular forms of integral weight

Citation

Yang, Yifan. Modular forms of half-integral weights on $\operatorname{SL}(2,\mathbb{Z})$. Nagoya Math. J. 215 (2014), 1--66. doi:10.1215/00277630-2684452. https://projecteuclid.org/euclid.nmj/1399554604


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