Why is my American Opportunity Credit $1,226?

Hi all. This is my first year filing taxes and I'm trying to work out why TurboTax is only able to claim $1,226 from the American Opportunity Credit. My expenses are easily high enough (over $10,000) for the maximum amount of $2,500. Now, I understand that a maximum of $1,000 is refundable. However, I'm not at this limit; my federal refund is only $399, so I should be able to get an additional $601. Is there some obvious bit of math I'm missing? Thanks!