There wouldnt be a bang in the electricity bill with a small light and heat rock for the reptile. Do you have any experience with pets? Are you responsible? Do you help your mother and make her feel that you are deserving of this? Are you ready for a pet?
Take that into consideration when asking her for permission. You might try to show that this would be a great learning experience and teach you responsibility. Find a reptile that isnt too needy, doesnt get large, doesnt stink, and doesnt cost too much. Price could be a concern so try to keep that to a minimum. We dont know the exact reasons that your mother is hesitant, but keep her feelings and concerns in mind as you convince her and prove to her that you are deserving and ready. When I lived with my mom, begging did not work... at all. I had to keep my cool and discuss things with her like an adult, as well as prove to her that I was prepared and deserving.
Good luck bro