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Multiplicities of representations in spaces of modular forms

Author(s): Bin Yong Hsie
Journal: Proc. Amer. Math. Soc. 134 (2006), 1-3.
MSC (2000): Primary 11F11
Posted: August 19, 2005
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Abstract: This paper shows that for a given irreducible representation $\rho$ of $\Gamma /\Gamma _{1}$ , the two functions dim( $M_{k}(\Gamma _{1},\rho )$ ) and dim( $S_{k}(\Gamma _{1},\rho )$ ) of are almost linear functions.

References:

1.: O. Forster, Lectures on Riemann Surfaces, Springer-Verlag, New York, 1981. MR 0648106 (83d:30046)
2.: N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer-Verlag, New York, 1984. MR 0766911 (86c:11040)
3.: J-P. Serre, Linear Representations of Finite Groups, Springer-Verlag, New York, 1977. MR 0450380 (56:8675)
4.: G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Princeton University Press, Princeton, New Jersey, 1971.

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Additional Information:

Bin Yong Hsie
Affiliation: LMAM, Department of Mathematics, Peking University, Beijing 100871, People's Republic of China
Email: byhsie@math.pku.edu.cn

DOI: 10.1090/S0002-9939-05-08289-4
PII: S 0002-9939(05)08289-4
Keywords: Modular form, cusp form
Received by editor(s): June 4, 2004
Posted: August 19, 2005
Communicated by: David E. Rohrlich
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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B.Y.Hsie, Multiplicities of representations in spaces of modular forms, Proceedings of the American Mathematical Society 134 (2006), 1-3.


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