General aviation Flight Instructor reported a NMAC while in the pattern. Instructor maneuvered his aircraft to avoid a collision.

Narrative

Was practicing patterns and landings with a student at ULM. Turned crosswind; then downwind; traffic entered the pattern behind us in the crosswind and proceeded to follow us in the downwind. We were continuously making position reports and queried the aircraft behind us if they had us in sight; as we could see them closing in on our position through ADSB at the same altitude; but they were behind us; and we could not visually see them. We did not receive a response. As we began our descent to land in the downwind; they had closed considerable distance on our location. We received a traffic advisory for that aircraft; and I decided to rapidly descend and bank left to avoid losing the required separation between our aircraft and the other aircraft. As I was flying this maneuver; the other aircraft proceeded to fly almost directly over top of us; approximately 400 feet above our altitude. Had it not been for this maneuver; I believe this situation could have led to a possible Mid-air collision. The local area was very congested with traffic at the time; and I believe that was a leading factor in the development of this scenario; as well as a lack of communication and possible lack of visual scanning from the other aircraft to see and avoid our aircraft.