Not big enough Virgil. For every 1000 watts, you need 10 amps of alternator.
You need:
Big 3 Upgrade (Gooogle it.)
Larger alternator
Possibly a spare battery.
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im sorta new to the audio world and experimenting on my own a lil bit...but do you use a good quality battery like the optima yellow or blue top....i run a yellow after hookin my system up and seems to work very well...
trevor