absolutly the box has everything to do with it. a larger box will give you deeper bass but if you get a ported box designed for that sub and port it correctly it will potentially have 3-6 db more than you have now and will also go significantly lower. 3-6 db would be equivelent to running 2 to 4 times as much power as you are runnng now.
if you want a correctly aligned box designed to fit your car check out my website in the link in my sig. i have a page that allows you to design the box you want, add features, make comments about how you want it and we will build it for you.