My boyfriend and I had twins last year and are wondering who should claim them? He didn't file last year and I only worked part of the year making around $10,000 or so.

We are not married and are new parents (to twin girls!) so we weren't certain what to do. I've always filed and taken care of my taxes and he unfortunately hasn't... I did withdraw a 401k of about $3300 and I only made just over $10,000 from employment income. Am I correct in thinking that I am the one who should claim them? Especially because he didn't file last year?