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Period polynomials and congruences for Hecke algebras

Published online by Cambridge University Press:  20 January 2009

Winfried Hohnen
Winfried Hohnen
Affiliation:
Mathematisches Institut, Universität Heidelberg, Im Neuenheimer feld 288, 69120 HeidelbergGermany
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Using the Eichler-Shimura isomorphism and the action of the Hecke operator T2 on period polynomials, we shall give a simple and new proof of the following result (implicitly contained in the literature): let f be a normalized Hecke eigenform of weight k with respect to the full modular group with eigenvalues λp under the usual Hecke operators Tp (p a prime). Let Kf be the field generated over Q by the λp for all p. Let p be a prime of Kf lying above 5. Then

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 2 , June 1999 , pp. 217 - 224
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

1.Deligne, P. and Serre, J.-P., Formes modulaires de poids 1, Ann. Sci. École Norm. Sup. 7 (4) (1974), 507–530.CrossRefGoogle Scholar
2.Hatada, K., Eigenvalues of Hecke operators on SL2(Z), Math. Ann. 239 (1979), 75–96.CrossRefGoogle Scholar
3.Kohnen, W. and Zagier, D., Modular forms with rational periods, in Modular Functions, (ed. Rankin, R. A., Ellis Horwood: Chichester 1984), 197–249.Google Scholar
4.Lang, S., Introduction to Modular Forms (Springer: Berlin-Heidelberg-New York 1976).Google Scholar
5.Manin, Yu, Periods of parabolic forms and p-adic Hecke series, Mat. Sb. 21 (1973), 371–393.CrossRefGoogle Scholar
6.Serre, J.-P., Valeurs propres des opérateurs de Hecke modulo l. Journées arith. Bordeaux, Astérisque 24–25 (1975), 109–117.Google Scholar
7.Zagier, D., Hecke operators and periods of modular forms, Israel Math. Conf. Proc. 3 (1990), 321–336.Google Scholar