Teenagers in nonabusive households have a few 'jobs' at home.
- Getting good grades
- Doing chores
- Not killing your sibling(s), if any
- Doing things like honoring a curfew
There are more but these are some of the bigger ones. Some kids may have to work and hand over some of their pay to keep a household going, but those first four are pretty big and they are pretty universal.
If you've messed up any of the big four, then you can (maybe) show your contrition by doing the others—and also
no longer doing the thing that was messed up. E.g. you get in after curfew, then your mission is to get in early. Your grades slip, then your mission is to get tutoring, study at home, go to the library, and otherwise show you're serious about your studies. If you're not doing chores, then your mission is to do what you're given to do with enthusiasm and pride, and to do more than the expected.
You get the idea.
Because even if you've never broken her trust, maybe it's something like this. Just not getting into trouble is not a very high standard, and many parents want their kids to do better and to be better.
You can also directly talk to her about it. And again, show her you're doing these other things.
"Mom, my homework and my chores are done. Dan (or any sibling's name, if applicable) should be okay if I keep headphones on. So, can you please loosen the controls so I can play __x___ game for a few hours? Here's what it looks like. I'll be in bed on time. Thanks!"
There are also parents who are overly obsessed with safety, or overdo it. And there are parents who are overly strict, and rigid to the point of being damaging to their kids. Your mother doesn't necessarily sound like any of these kinds of parents.
So... ask! But do so armed with that kind of backing. Just asking her to loosen the controls so you can play video games all day and night is not going to be a good look if the dishes are piled in the sink, your homework isn't done, your grades are slipping, and you were late coming home last week.
This is called arguing from a position of strength, versus a position of weakness.
Oh, and one more thing. Since you've obviously used your aunt's computer to circumvent these kinds of restrictions before, that may very well be your problem right there. Can you see your mother's perspective on that? It's her laying down a rule, and then you thumbing your nose at her and violating it anyway.
That's kinda the definition of breaking trust.