Hybrid sup-norm bounds for Hecke-Maass cusp forms

Let f be a Hecke-Maass cusp form of eigenvalue lambda and square-free level N. Normalize the hyperbolic measure so that vol (Y-0(N)) = 1 and the form f such that parallel to f parallel to(2) = 1. It is shown that parallel to f parallel to(infinity) <<epsilon lambda(5/24+epsilon) N1/3+epsilon for all epsilon > 0. This generalizes simultaneously the current best bounds in the eigenvalue and level aspects.