Hi im 15m and my ex/friend is 17f we broke a month ago because I screwed up how can i make her love me and trust me again

So me and my ex broke up about month ago and in that month she still loved me and cared about me but i did something i really regret while we were together i talked to a old friend of mine behind her back which really hurt her but she forgave me and told me to never do it again if i did i would lose her forever
But i did it again not even because i wanted to talk to my old friend i felt bad for her cause her dad died but my ex found out and it made her loose all feelings for me no love no respect no empathy we are just friends now but i said to her i will back off for one year and change she said okay she says its impossible and she respects herself enough to not do it again how can i prove to her that i have changed and will change and make her love me again she also said she emotionally de attached from me but she aslo said it just come back some time we are long distance too but when we were together we were both so happy how can i make her see that she can love me again and not regret it