Modern day dimmers have a solid state device in them called a triac. The triac is basically a very fast acting switch that cuts the half wave cycle time (on verses off) to dim a lamp. The more you dim, the more of the 1/2 cycle wave is in the off position. Of course the triac deals with both sides of the sinewave. This fast switching may cause hum if the lighting circuit is part of the outlet branch circuit. There are filters out there, but the success rate is by trial and error.
An alternative is to remove the dimmer and replace the lamp with a lower lumin output that matches your usual dimming level, or separate the lighting from the outlet on the branch circuits (and that may not even help). Certainly avoid any style of CFL lamps, but I have noticed that I can read my strobe disc with the current LEDs in my vinyl room....so what does that tell ya?
I suggest that you eliminate the problem and if you can't deal with the solution, find a different way to accomplish the same thing. If you are using LEDs in your room, you should use a high quality "CL" dimmer that are made to handle not only incandescent but LEDs and CFLs (that are dimmable).
You can also reduce light output by mechanical means, like a perforated metal screen or the use of opaque objects to block a portion of the lamp output. Care must be taken so as not to overheat the lamp of the fixture it is in.
