Understandable. Maybe it's not right on that page. But yeah, you should be fine to submit.
...could it possibly be 4Mx4M pix?! That'd be one friggin big picture!!! Of course, knowing Newgrounds, it could be a sarcastic exaggeration. That 'raytracing' pic below is over 6000 pix and it slows my computer down, even at small size, so be aware that bigger isn't always a good thing. You can only see a tiny corner when it's that large anyway!
Exedor
...2000x2000? You sure?
http://www.newgrounds.com/art/view/mckodem/bayonetta-chibi
http://www.newgrounds.com/art/view/gairon/summer-festival-girls
http://www.newgrounds.com/art/view/ravengrad/aigis
http://www.newgrounds.com/art/view/jonwing/purgatory
http://www.newgrounds.com/art/view/fiomeria/paz-the-wolf-woman
And, the king:
http://www.newgrounds.com/art/view/arkanrais/goddamn-raytracing
I suppose you could remove the upper part of the building, as there's not really much going on up there. Still, obviously, there are other pics on here that blaze past the 2000x2000 mark. The biggest problem with them is what ends up being visible onscreen when it's brought to full size. With that pic, tho, you should be fine.
Flashlight237
I was pretty much sure of it. At least that's what the "Submit Your Work" form is telling me. When I looked, the form said "Image must be between 16x16 px and 4 million px square", which I believed meant "16x16 px to 2000x2000 px."