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2010 Modular Forms on Noncongruence Subgroups and Atkin--Swinnerton-Dyer Relations
Liqun Fang, J. William Hoffman, Benjamin Linowitz, Andrew Rupinski, Helena Verrill
Experiment. Math. 19(1): 1-27 (2010).


We give new examples of noncongruence subgroups $\Gamma\subset\SL_2(\Z)$ whose space of weight-3 cusp forms $S_3(\Gamma)$ admits a basis satisfying the Atkin--Swinnerton-Dyer congruence relations with respect to a weight-3 newform for a certain congruence subgroup.


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Liqun Fang. J. William Hoffman. Benjamin Linowitz. Andrew Rupinski. Helena Verrill. "Modular Forms on Noncongruence Subgroups and Atkin--Swinnerton-Dyer Relations." Experiment. Math. 19 (1) 1 - 27, 2010.


Published: 2010
First available in Project Euclid: 12 March 2010

zbMATH: 1225.11049
MathSciNet: MR2649983

Primary: 11F11 , 11F33 , 11G40 , 14J27

Keywords: Atkin--Swinnerton-Dyer relations , modular forms , noncongruence subgroups

Rights: Copyright © 2010 A K Peters, Ltd.

Vol.19 • No. 1 • 2010
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