First moments of central L-values

We consider first moment averages of central L-values in cases where the Dirichlet coefficients factor. Such as the case of a Rankin-Selberg convolution of two modular forms or a modular form twisted by a Dirichlet character. In either case, the level aspect bounds one obtains through classical analytic tools are analogous in terms of the individual conductors of each object in the convolution. When one has positivity of the central L-values, hybrid subconvexity results are established. This suggests that perhaps the arithmetic nature of the conductor alone, rather than the complexity of the representation, is the important ingredient in establishing such bounds.