What would she have to do for you to take her back?

Short story: I've been in a long distance relationship with my boyfriend for 2 1/2 years. (We were set to move to the same city next summer.) A few weeks ago, we had a disagreement and he dumped me over the phone. I was so hurt, frustrated, and upset that all I wanted to do was forget about him as easily as he had forgotten about me so I slept with someone else. (Don't worry ... trust me ... I regretted it the very second I did it.) Hours later my boyfriend and I got back to together and he said he dumped me in the heat of the moment and didn't mean it. I didn't tell him what happened between me and the other person until 2 weeks later over the phone. My boyfriend was so hurt that he said it was over between us. That same day, I immediately booked a plane ticket to his city to see him in person, express my heartfelt apology face to face, etc. He did see me and hear me but still said it was over.

I know what I did was awful and very, very stupid. I don't need further beating up about it. I am genuinely sorry and have never been unfaithful to him or anyone else before. I know he is hurting right now and the last thing he wants is to be bothered. Our relationship was filled with a lot of love and trials and I just know deep in my heart that if we could work through this I would never hurt him again. I am not asking anyone to bash/analyze me for what I did. I ask:

What can I do for him to trust me again and forgive me? Should I just leave him alone right now? Should I drop hints that I still care (letters, cards)? What would a girl who has done this to you have to do for you to forgive her, trust her again, and want to work through this?
Updates:
+1 y
Thanks guys and girls. He still says it's over. (Been 1 1//2 weeks now.) I've decided to let it go. He knows that I love him dearly and am sorry, but he can't remove the image from his head. I'm realizing I wasn't entirely listened to anyway.
+1 y
The event happened on a night when he said he was going out of town at the last minute and refused to talk to me on the phone while he was in the car with his brother and friend. (He agreed to talk a bit before driving off and a bit when he got there.)
+1 y
We couldn't compromise and he eventually called it quits. Though the mistake I made has potentially broken us up for good, looking back at our relationship, I think his inability to sometimes understand my side would have separated us eventually.
What would she have to do for you to take her back?
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