A simplified trace formula for Hecke operators for $\Gamma _ 0(N)$
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- by Shepley L. Ross PDF
- Trans. Amer. Math. Soc. 331 (1992), 425-447 Request permission
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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Additional 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