A4,My rear left turn signal will not work and I have replaced the bulb and checked the fuse.

In my audi, my rear left turn signal does not work. The front left and both signals on the right side all work. The front left blinks faster in oder to compensate. I have replaced the bulb but that did not work. I checked the fuse and they are all fine. I checked the socket and it looks clean. I am not sure what else to do.
My car has an automatic transmission.