Personally, I'm finding this to be a very interesting discussion. On one hand, you should do what your parents tell you and listen to them because they know what's best. But, on the other hand, you can't let them control your life and, well, sometimes they don't always know what is best, if that makes sense.
Kinda like that saying "If everyone else jumps off a cliff, will you?"
Basically what I'm trying to say is that you should listen to your parents but you shouldn't do EVERYTHING they tell you to.
I think you should talk to your mom about it and I agree with maybe asking her to talk to your dad.
When I wanted a betta, I spent 9 months of keeping my room clean, doing loads of chores, and showing my parents betta sites (including this one) and randomly telling them betta facts to prove I knew what I was talking about. For me, the reason why it was a no is because my mom had bettas and other fish her whole life and hated cleaning the aquariums and didn't want to have to deal with one again. She didn't seem to realize that I AM 15 and can do this on my own and can make money to buy things my betta needs. My dad didn't want any pets in this house because he's just kinda a no-pet no-animal person. Which is sad because I love all animals and wish it was possible for one person to learn everything about every animal, because I'd love to do that. Anyways, my point is, I showed my parents I was mature and could do it and would work hard to do it and, eventually, they agreed and last Summer I got my first betta.
Anyways, long story short, try being like the best child ever for a while and talk to your mom about it :) Unless there's some real big reason why they say no, you should be able to convince them ;)
P.S. You're 15 too?