  The purpose of this article is to show how the root number of a modular form
changes by twisting in terms of the local Weil-Deligne representation at each
prime ideal. As an application, we show how one can for each odd prime $p$,
determine whether a modular form (or a Hilbert modular form) with trivial
nebentypus is Steinberg, Principal Series or Supercuspidal at $p$ by analyzing
the change of sign under a suitable twist. We also explain the case $p=2$,
where twisting is not enough in general.
