  Let $f$ be a weight $k$ holomorphic cusp form of level one, and let $S_f(n)$
denote the sum of the first $n$ Fourier coefficients of $f$. In analogy with
Dirichlet's divisor problem, it is conjectured that $S_f(X) \ll
X^{\frac{k-1}{2} + \frac{1}{4} + \epsilon}$. Understanding and bounding
$S_f(X)$ has been a very active area of research. The current best bound for
individual $S_f(X)$ is $S_f(X) \ll X^{\frac{k-1}{2} + \frac{1}{3}} (\log
X)^{-0.1185}$ from Wu. Chandrasekharan and Narasimhan showed that the Classical
Conjecture for $S_f(X)$ holds on average over intervals of length $X$. Jutila
improved this result to show that the Classical Conjecture for $S_f(X)$ holds
on average over short intervals of length $X^{\frac{3}{4} + \epsilon}$.
Building on the results and analytic information about $\sum \lvert S_f(n)
\rvert^2 n^{-(s + k - 1)}$ from our recent work, we further improve these
results to show that the Classical Conjecture for $S_f(X)$ holds on average
over short intervals of length $X^{\frac{2}{3}}(\log X)^{\frac{1}{6}}$.
