  We consider a $\mathbb{R}^d$-valued branching random walk with a stationary
and ergodic environment $\xi=(\xi_n)$ indexed by time $n\in\mathbb{N}$. Let
$Z_n$ be the counting measure of particles of generation $n$. With the help of
the uniform convergence of martingale and the multifractal analysis, we
establish a large deviation result for the measures $Z_n$ as well as a moderate
deviation principle.
