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Relations between cusp forms on congruence and noncongruence groups


Author: Gabriel Berger
Journal: Proc. Amer. Math. Soc. 128 (2000), 2869-2874
MSC (1991): Primary 11F11; Secondary 11F30
DOI: https://doi.org/10.1090/S0002-9939-00-05476-9
Published electronically: April 7, 2000
MathSciNet review: 1695104
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Abstract | References | Similar Articles | Additional Information

Abstract: We construct a quadratic relation between cusp forms of weight two on four genus $1$ subgroups of $SL_2(\mathbb{Z} )$. Two of the subgroups are congruence and two are noncongruence. We then generalize this to subgroups of $\Gamma (N)$ of index 2.


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Additional Information

Gabriel Berger
Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467
Address at time of publication: Alphatech, Inc., 50 Mall Rd., Burlington, Massachusetts 01803
Email: gberger@channel1.com

DOI: https://doi.org/10.1090/S0002-9939-00-05476-9
Keywords: Noncongruence subgroup, cusp form
Received by editor(s): November 16, 1998
Published electronically: April 7, 2000
Additional Notes: The author was supported in part by JSPS grant P94015 and NSA grant 032596.
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2000 American Mathematical Society

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