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- W1785325206 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 {eta(24tau)^rf(24tau):f(tau)in M_s(1)} is isomorphic to S_{r+2s-1}^{text{new}}(6,-(frac8r),-(frac{12}r))otimes(frac{12}cdot) as Hecke modules under the Shimura correspondence. Here $M_s(1)$ denotes the space of modular forms of weight $s$ on $Gamma_0(1)=mathrm{SL}(2,Z)$, $S_{2k}^{text{new}}(6,epsilon_2,epsilon_3)$ is the space of newforms of weight $2k$ on $Gamma_0(6)$ that are eigenfunctions with eigenvalues $epsilon_2$ and $epsilon_3$ for Atkin-Lehner involutions $W_2$ and $W_3$, respectively, and the notation $otimes(frac{12}cdot)$ means the twist by the quadratic character $frac{12}cdot)$. There is also an analogous result for the cases $(r,6)=3$." @default.
- W1785325206 created "2016-06-24" @default.
- W1785325206 creator A5070793507 @default.
- W1785325206 date "2011-10-09" @default.
- W1785325206 modified "2023-09-24" @default.
- W1785325206 title "Modular forms of half-integral weights on SL(2,Z)" @default.
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- W1785325206 doi "https://doi.org/10.48550/arxiv.1110.1810" @default.
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