Bounds for twisted symmetric square LL-functions—III

Let ff be a Hecke modular form, and let χχ be a primitive character of conductor qℓqℓ. Assume that qq is an odd prime. In this paper we prove the subconvex bound L(12,Sym2f⊗χ)≪f,q,εq3ℓ(14−136+ε) for any ε>0ε>0. This can be compared with the recently established tt-aspect subconvexity of the symmetric square LL-functions.