First moment of Rankin–Selberg central L-values and subconvexity in the level aspect

Let 1≤ N < M with N and M coprime and square-free. Through classical analytic methods we estimate the first moment of central L -values where runs over primitive holomorphic forms of level N and trivial nebentypus and g is a given form of level M . As a result, we recover the bound when g is dihedral. The first moment method also applies to the special derivative under the assumption that it is non-negative for all .