Conjecture on coefficients attached to closed orbits in automorphic representations

Let $\mathcal O$ be a fixed closed orbit, and let $a_{n,\lambda}$ be the coefficients in the expansion associated with $\mathcal O$ and the representation parameter $\lambda$. Closed-orbit coefficient conjecture. For any $\varepsilon>0$,

$$\left|a_{n,\lambda}\right|\ll\left(\max\\{|n|,|\lambda|\\}\right)^\varepsilon.$$

The conjecture seeks a Ramanujan-type subpower bound for individual coefficients, whereas the theorem preceding it gives only a sharp average bound; no resolution is stated in the supplied text.