Back in the day (dawn?) I was a big Joy Division fan*, I didn't catch New Dawn Fades, now I'll have to listen out for it.Which one? I reckon you are referring to "God Moving Over the Face of the Waters", which is used brilliantly for the finale of the film - but Moby's "New Dawn Fades" is also used: it is a version of a Joy Division song, and it is the music used when Hanna is tailing McCauley prior to their coffee shop chat.
*Fan is the wrong word. Joy Division was almost a religious experience for those living in Thatcher's Britain. Perhaps others know of similar poetry coming out of desperation, depression and epilepsy but you really have to live thru it to appreciate it.