  Fix $g$ a self-dual Hecke-Maass form for $SL_3(\mathbb{Z})$. Let $f$ be a
holomorphic newform of prime level $q$ and fixed weight. Conditional on a lower
bound for a short sum of squares of Fourier coefficients of $f$, we prove a
subconvexity bound in the $q$ aspect for $L(s, g\times f)$ at the central
point.
