What should I do about her?

My girlfriend told me to break up because she was cheating on me,even though I love her,I did broke up because I can't stand this kind of betrayal,I mean she seemed happy with her new guy,anyway,now he dumbed her and she returned to me asking me to accept her back and that if I love her I should forgive her,I love her but I feel confused,I mean what should I do?I don't want to let her down but it doesn't seem right to accept her back either...?