Dimmers are notorious in terms of dirtying up AC. Do you have a hum with the dimmer switch completely off (or, conversely, all the way up)? If not, then it's the dimmer switch. If you still have a hum, troubleshoot as the posts above advise and try to isolate which component may be the source.
You can have an electric company in your area run a dedicated line from your wall outlet to your circuit breaker for fairly cheap. That way you amps will draw power meant for them and for them only.
You can have an electric company in your area run a dedicated line from your wall outlet to your circuit breaker for fairly cheap. That way you amps will draw power meant for them and for them only.