  Let $f$ be a Hecke-Maass or holomorphic primitive cusp form of arbitrary
level and nebentypus, and let $\chi$ be a primitive character of conductor $M$.
For the twisted $L$-function $L(s,f\otimes \chi)$ we establish the hybrid
subconvex bound $$ L(1/2+it,f\otimes\chi)\ll (M(3+|t|))^{1/2-1/18+\varepsilon},
$$ for $t\in \mathbb R$. The implied constant depends only on the form $f$ and
$\varepsilon$.
