Ex troubles 26M and 24F

Me 26M and my girlfriend 24F have been together for about 4 months. Everything is seemingly really good but near the start of the relationship she told me she still was talking to her ex of 3 years. I told her I wasn’t comfortable with that because of the abusive past they had. After a couple months, we were going through pictures on her phone and I saw that they were having sex just a little bit before we started talking and also I saw some pictures of her with her ex at her house from a month before I saw the pictures and he was shirtless. She said that’s just how he was “slobby” and she really regretted it. I asked her if they were doing anything since before then and she said since he was homeless, he would stay at her house and I asked if they had sex and she said they just slept together but she didn’t let him have sex, but they haven’t done that in awhile. Also she said she’s been hurt a lot so she didn’t know if she fully trusted me yet at the start. She said he felt like family and didn’t want to let him go but wouldn’t deny having feelings for him when I asked. She said he’s in jail now and that’s good cause it gives them space. I said so if he’s not in jail, he would still be coming over? She said no it’s different now, she wouldn’t let him come over anymore if that happened. I love her very much but I told her I forgive her for my own peace. It’s been a month now and we do very good together, but it’s still on my mind and I’m wondering if I should break it off?

tl;dr girlfriend previously talking to ex but said she’s not anymore. Idk if I should break it off.