What type of pet is right for me?

A dog or a cat is off limits. I've looked into lots of different types of pets but I have yet to find one that is right for me. I want an odorless pet but I don't want a fish or a turtle, I want a social pet. I don't want a pet that requires huge amounts of care but I'm willing to care for it. I cannot get a bird, and I am not exactly a fan of reptiles. I also don't like rodents that much. I looked into rabbits but my mother vetoed that one. Please help if you have any alternate suggestions, I just want a pet so bad but I want one that is right for me.