Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
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.


References [Enhancements On Off] (What's this?)

  • [B] G. V. Belyĭ, Galois extensions of a maximal cyclotomic field, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), no. 2, 267–276, 479 (Russian). MR 534593
  • [Be] Gabriel Berger, Hecke operators on noncongruence subgroups, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), no. 9, 915–919 (English, with English and French summaries). MR 1302789
  • [F] Fricke, R. Lehrbuch der Algebra vol 2, 1926,Vieweg and Son, Braunschweig.
  • [S] A. J. Scholl, Modular forms and de Rham cohomology; Atkin-Swinnerton-Dyer congruences, Invent. Math. 79 (1985), no. 1, 49–77. MR 774529, 10.1007/BF01388656
  • [Sh] Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. Kan\cflex o Memorial Lectures, No. 1. MR 0314766

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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: http://dx.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