Hybrid subconvexity bounds for L12,Sym2f⊗g

Fix an integer κ ⩾ 2 . Let P be prime and let k > κ be an even integer. For f a holomorphic cusp form of weight k and full level and g a primitive holomorphic cusp form of weight 2 κ and level P , we prove hybrid subconvexity bounds for L 1 2 , Sym 2 f ⊗ g in the k and P aspects when P 13 64 + δ < k < P 3 8 - δ for any 0 < δ < 11 128 . These bounds are achieved through a first moment method (with amplification when P 13 64 < k ⩽ P 4 13 ).