you could check a few things...

1) check the gauge strings your using.. I tried a higher gauge on mine and I got the infamous post of "gstring buzzin at the nut!"

once I changed the strings, it was fixed..

2) check the nut, maybe it needs a little graphite lube on it.. be careful with this stuff, it's slippery as hell on the fretboard

3) check your bridge, loose saddles, incorrect intonation

lastly, that familiar fender hum is from no insulation on the wires..

if you take off the pick guard, you'll see.. some people spray an insulation paint in there and then clean up the wires so that doesn't happen.. a buddy did it to a squire strat and it worked pretty well...