Hi, everyone, I want to ask a question about line bundle.

Let $X$ be a smooth curve over a algebraically closed field $k$, and $f:Y \longrightarrow X$ a Galois finite etale covering with Galois group $G$ and degree $n$. Suppose that $L$ is a line bundle on $X$.

Dose there exist a line bundle $M$ on $Y$ such that $M^{\otimes n}=f^{*}L$?

Thanks.