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Relations between cusp forms on congruence and noncongruence groups
Author(s):
Gabriel
Berger
Journal:
Proc. Amer. Math. Soc.
128
(2000),
2869-2874.
MSC (1991):
Primary 11F11;
Secondary 11F30
Posted:
April 7, 2000
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Abstract:
We construct a quadratic relation between cusp forms of weight two on four genus  subgroups of  . Two of the subgroups are congruence and two are noncongruence. We then generalize this to subgroups of  of index 2.
References:
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- [B]
- Belyi, G.V. On the Galois Extensions of the Maximal Cyclotomic Field 1979, Izv. Akad. Nauk. SSSR, vol 43, pp. 267-276. MR 80f:12008
- [Be]
- Berger, G. Hecke Operators on Noncongruence Subgroups 1994, C.R. Acad Sci, Paris, t 319, Series 1, pp. 915-919. MR 95k:11063
- [F]
- Fricke, R. Lehrbuch der Algebra vol 2, 1926,Vieweg and Son, Braunschweig.
- [S]
- Scholl, A.J. Modular Forms and de Rham Cohomology; Atkin-Swinnerton-Dyer congruences Invent. Math., vol 79, pp. 49-77. MR 86j:11045
- [Sh]
- Shimura, G. Introduction to the Arithmetic Theory of Automorphic Functions Iwanami Shoten, 1971. MR 47:3318
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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:
10.1090/S0002-9939-00-05476-9
PII:
S 0002-9939(00)05476-9
Keywords:
Noncongruence subgroup,
cusp form
Received by editor(s):
November 16, 1998
Posted:
April 7, 2000
Additional Notes:
The author was supported in part by JSPS grant P94015 and NSA grant 032596.
Communicated by:
David E. Rohrlich
Copyright of article:
Copyright
2000,
American Mathematical Society
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