Let $E_1/\Q, \ldots, E_g/\Q$ be elliptic curves over $\Q$, without complex multiplication and pairwise non-isogenous over $\overline{\Q}$. For an integer $t$ and a positive real number $x$, denote by $\pi_A(x, t)$ the number of primes $p \leq x$, of good reduction for the abelian variety $A := E_1 \times \ldots \times E_g$, for which the Frobenius trace associated to the reduction of $A$ modulo $p$ equals $t$. We present unconditional and conditional upper bounds for $\pi_A(x, t)$. This is joint work with Tian Wang (University of Illinois at Chicago).