## Abstract

We establish a simple inductive formula for the trace $Trknew(Γ0(8),p)$ of the pth Hecke operator on the space $Sknew(Γ0(8))$ of newforms of level 8 and weight k in terms of the values of 3F2-hypergeometric functions over the finite field Fp. Using this formula when k = 6, we prove a conjecture of Koike relating $Tr6new(Γ0(8),p)$ to the values 6F5(1)p and 4F3(1)p. Furthermore, we find new congruences between $Trknew(Γ0(8),p)$ and generalized Apéry numbers.