There must be specific behaviors that cause you to suspect that she's still got a thing for her ex. For example, she may bring him up in conversation a fair amount, she's holding on to their relationship memorabilia, the posts she makes on social media, etc.
When there's a good time, discuss it with her in person (so you can read her facial expressions and other nonverbal behaviors). Tell her that you've noticed that she's brought his name up three times in your date today (or whatever the behavior is), then nonjudgmentally ask if she is having trouble getting over him. People can't always turn off their feelings when they break up with someone, especially if the relationship ended badly. She may need some time and understanding. If you are willing to be patient, then ask her what she needs from you. She may be into you but just need to take a new relationship a little slow, especially if she was really in love with him, he betrayed her, and/or dated him a long time. Talk about it. If you like her invest in the relationship.