The fourth moment of holomorphic Hecke cusp forms in shorter intervals

Let $0<c\le 1\mathrm{/}4$ be fixed. For $H=K^{\frac{3}{4}+c}$, we find the average value of the fourth moment of holomorphic Hecke cusp forms of weight varies within $[K,K+H]$, improving a previous result of Khan.