## Abstract

Let $f(z)=∑a(m)m(k−1)/2e(mz)∈Sk(N,χ1)$ be a primitive cusp form of integral weight k, level N, and character χ1. For a smooth weight function g with compact support in $[M1,2M1]×[M2,2M2]$ and positive integers l1, l2, h, the bound $∑l1m1−l2m2=ha(m1)a(m2)¯g(m1,m2)1≪ε(l1M1+l2M2)1/2+θ+ε$ with θ = 7/64 is shown. As an application, the shifted sum $∑m≤Ma(m)a(m+h)¯$ is bounded nontrivially for $h≪M64/39−ε$. Furthermore, the subconvexity bound $Lf(1/2+it,χ)≪εD71/167+ε$ for the L-function attached to the twist of f with a primitive character χ to modulus D is obtained.