If I say, $f|_{k}$, what does that mean?

If I say, $f|_{k}$, what does that mean? Sorry to be short on words but I can not find it anywhere on google so maybe someone could explain it and what we typically use it for. I ran into the notation in a book and they do not explain what it is.

• In what book did you run into this notation? – awllower Oct 22 '14 at 0:47

It means that if $f$ is defined on the set $X$, and $k \subseteq X$, then $f|_k$ is $f$ restricted to the set $k$.
It might also have the meaning that $f$ is a modular form, and $k\in\operatorname{SL}_2(\mathbb Z),$ and $f\mid_k$ is $f$ under the action of $k.$