TITLE: BSD for modular forms
QUESTION [12 upvotes]: Given a modular form, what is the precise formulation of BSD (in particular, the residue formula for the $L$-function at special values)? And what about the special values if the $L$-function is twisted by some character? Does there exist a good reference?

REPLY [3 votes]: This paper http://wstein.org/papers/motive_visibility/ by Dummigan, me, and Watkins gives a  detailed answer to your question.  Plus it has some explicit examples of weight 4 modular forms so that the corresponding motive conjecturally has nontrivial (visible) Shaferevich-Tate group.