Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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A simplified trace formula for Hecke operators for $\Gamma _ 0(N)$
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by Shepley L. Ross
Trans. Amer. Math. Soc. 331 (1992), 425-447
DOI: https://doi.org/10.1090/S0002-9947-1992-1053115-1

Abstract:

Let $N$ and $n$ be relatively prime positive integers, let $\chi$ be a Dirichlet character modulo $N$, and let $k$ be a positive integer. Denote by ${S_k}(N,\chi )$ the space of cusp forms on ${\Gamma _0}(N)$ of weight $k$ and character $\chi$, a space denoted simply ${S_k}(N)$ when $\chi$ is the trivial character. Beginning with Hijikata’s formula for the trace of ${T_n}$ acting on ${S_k}(N,\chi )$, we develop a formula which essentially reduces the computation of this trace to looking up values in a table. From this formula we develop very simple formulas for (1) the dimension of ${S_k}(N,\chi )$ and (2) the trace of ${T_n}$ acting on ${S_k}(N)$.
References
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Bibliographic Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 331 (1992), 425-447
  • MSC: Primary 11F11; Secondary 11F25, 11F72
  • DOI: https://doi.org/10.1090/S0002-9947-1992-1053115-1
  • MathSciNet review: 1053115