On triple correlation sums of Fourier coefficients of cusp forms

Let p be a prime. In this paper, we study the sum sigma (m >= 1) sigma (n >= 1 ) a(n)lambda(g)(m)lambda(f)(m + pn) U(m/X) V (n/H) for any newforms g is an element of B-k(1) (or B*(lambda)(p)) and f E Bk(p) (or B*lambda(p)), with the aim of determining the explicit dependence on the level, where a = {a(n) is an element of C} is an arbitrary complex sequence. As a result, we prove a uniform bound with respect to the level parameter p, and present that this type of sum is non-trivial for any given H, X >= 2.