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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Multiplicities of representations in spaces of modular forms
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by Bin Yong Hsie PDF
Proc. Amer. Math. Soc. 134 (2006), 1-3 Request permission

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 $k$ are almost linear functions.
References
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  • Neal Koblitz, Introduction to elliptic curves and modular forms, Graduate Texts in Mathematics, vol. 97, Springer-Verlag, New York, 1984. MR 766911, DOI 10.1007/978-1-4684-0255-1
  • Jean-Pierre Serre, Linear representations of finite groups, Graduate Texts in Mathematics, Vol. 42, Springer-Verlag, New York-Heidelberg, 1977. Translated from the second French edition by Leonard L. Scott. MR 0450380, DOI 10.1007/978-1-4684-9458-7
  • 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
  • MR Author ID: 769423
  • Email: byhsie@math.pku.edu.cn
  • Received by editor(s): June 4, 2004
  • Published electronically: August 19, 2005
  • Communicated by: David E. Rohrlich
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 1-3
  • MSC (2000): Primary 11F11
  • DOI: https://doi.org/10.1090/S0002-9939-05-08289-4
  • MathSciNet review: 2170535