Average values of symmetric square $L$-functions at the edge of the critical strip

Let ${\mathcal{B}}_{2}^{*}(N)$ be the set of all normalized newforms of weight 2 and level $N$, and let $L({\operatorname{sym}}^{2}f, 1)$ be the symmetric square $L$-function associated to $f\in {\mathcal{B}}_{2}^{*}(N)$. If $N$ is a prime, then there is a positive constant $B$ such that

This improves a recent result of Akbary, which requires $45/46$ in place of $27/28$.