Are you sure you can't take him home with you? Most apartments won't allow cats or Dogs but don't mind fish....it's not like they will get out and tear stuff up,bite the neighbors and poop all over...seriously ..maybe your Mom could ask him(her) and make sure taht restriction includes fish
Landlords sometimes have limits on the size of the tank (to prevent water damage) but there's no reason he shouldn't let a betta fish, unless he doesn't allow pitchers of water or potted plants either :P
In fact, dorm rooms, which are notoriously anti-pet allow fish tanks. You should really be pissed if he won't allow your fish.
I live on the 3rd floor and my biggest tank is a 29 gallon, which they know is in here, plus a 20 gallon and two other smaller tanks. So I'd revisit the issue with the landlord and see if the no-pet rule does in fact extend that far.