Can I finance a car with a 526 credit score and no co-signer?

I'm in my late 20's and right out of HS I moved half way across the country, knowing nothing I racked up a lot of credit and even had an eviction. Now I have managed to pay off most of my high balance cards and a few small ones. My credit score now is about 520 to 526, I have student loans all in good standing and 2 credit cards that are fairly new but also in good standing. I went from having about 25 to 30 negative accounts to having 9 good (6 being student loans, 2 capitol one MasterCard's and my current vehicle) and 8 that are still negative that I am still paying off one at a time. I still owe about $2,500 on my vehicle and make about $2,450 a month full time. I want to put $500 down as well as trade in my vehicle which has a Kelley Blue Book trade in value of $3,700 (Im hoping to get at least $2,800 though). I am not looking for anything over $16,000 is it possible to get financed for that or less without requiring a co-signer? FYI My current vehicle was co-signed by my ex and I have no family to co-sign so I need to be financed on my own.