Amp turns off when headlights turn on
 

I have a 2002 Mazda protege completely stock except for new headlights. I installed a 400w mdx amp in my trunk using 4 gauge wire. However when my headlights or even just the fog lights are turned on the amp turns off. If I turn the dimmer all the way down the amp turns on but puts out hardly any power. Do I need a new alternator to push my sound system? I also have a new stereo and new front door and rear speakers