Abstract
We provide formulas for traces of p t h p^{th} Hecke operators in level 1 in terms of values of finite field 2 F 1 _2F_1 -hypergeometric functions, extending previous work of the author to all odd primes p p instead of only those p ≡ 1 ( mod 12 ) p \equiv 1 \pmod {12} . We first give a general level 1 trace formula in terms of the trace of Frobenius on a family of elliptic curves, and then we draw on recent work of Lennon to produce level 1 trace formulas in terms of hypergeometric functions for all primes p > 3 p > 3 .
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