A simplified trace formula for Hecke operators for

Author:
Shepley L. Ross

Journal:
Trans. Amer. Math. Soc. **331** (1992), 425-447

MSC:
Primary 11F11; Secondary 11F25, 11F72

MathSciNet review:
1053115

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Abstract: Let and be relatively prime positive integers, let be a Dirichlet character modulo , and let be a positive integer. Denote by the space of cusp forms on of weight and character , a space denoted simply when is the trivial character. Beginning with Hijikata's formula for the trace of acting on , 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 and (2) the trace of acting on .

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DOI:
https://doi.org/10.1090/S0002-9947-1992-1053115-1

Keywords:
Cusp forms,
Hecke operators,
modular forms,
trace formula

Article copyright:
© Copyright 1992
American Mathematical Society