  Let $f$ be a holomorphic modular form of prime level $p$ and trivial
nebentypus. We show that there exists a computable $\delta>0$, such that $$
L\left(\tfrac{1}{2},\mathrm{Sym}^2 f\right)\ll p^{\tfrac{1}{2}-\delta}, $$ with
the implied constant depending only on $\delta$ and the weight of $f$.
