LAUSR

Abstract Let M be a square-free integer and P be a prime such that ( P , M ) = 1 . We prove a new hybrid bound for L ( 1 2 , f ⊗ g ) where f is a primitive holomorphic cusp form of level M and g a primitive (either holomorphic or Maass) cusp form of level P satisfying P ∼ M η with 0 η 2 / 15 . Particularly in the range β η ( 2 − 32 β ) / 15 with β = 11 / 4875 we present a strengthened level aspect hybrid subconvexity bound for L ( 1 2 , f ⊗ g ) relative to the current bounds obtained by Holowinsky–Munshi [11] and Ye [27] .