Second moment of $\textrm{GL(3)} \times \textrm{GL(2)}$ $L$--functions

For $M_1$ and $M_2$ two distinct primes, let $H_k^\star(M_1M_2, \psi)$ denote the set of primitive newforms of level $M_1M_2$, weight $k\geq 3$ and Nebentypus $\psi$ of conductor $M_1$. Let $\pi$ be a fixed $SL(3, \mathbb{Z})$ Hecke cusp form. We prove a Lindel\"of--consistent upper bound for the second moment $$\mathop{ \sum_{\substack{\psi(M_1) \\ \psi(-1)=(-1)^k }}} \sideset{}{^h}\sum_{f \in H_k^{\star}(M_1M_2,\psi)} |L(1/2, \pi \times f)|^2 \ll_{\pi,\epsilon} M_1^{1+\epsilon}$$ in the range $M_2\leq M_1^{1+\epsilon}$.