This is an army-cut overcoat that has been issued to an SS-Sturmmann.  It has no markings, is expertly tailored, and is ready for shoulder boards and collar tabs (not common on overcoats, but occasionally present).  Eagle is and rank chevron are sewn down rather roughly, indicating to me they are original to the jacket (what restoration person would do such a rough job).  Also, the lack of shoulder boards - someone creating a uniform for display would have installed SS enlisted shoulder boards - not at all hard to find.  In any case, a nice display piece that, when accompanied by a belt and visor, will look quite impressive!