Atkin–Serre lower-bound conjecture for Ramanujan's tau function

Let $\tau(p)$ denote the Ramanujan tau function evaluated at a prime $p$.

Atkin–Serre conjecture. For every $\varepsilon>0$, there exist constants $c(\varepsilon),d(\varepsilon)>0$ such that, for all primes $p>d(\varepsilon)$,

$$|\tau(p)|\ge c(\varepsilon)p^{\frac{9}{2}-\varepsilon}.$$

The source presents this as a stronger statement that would be needed to prove $|\tau(n)|\ge 100$ for $n>2$. It does not give a resolution of the conjecture.