Entering the Mercedes-Benz Superdome with a bag might not be a good idea and chances are that you will be turned away unless you obey the specific rules for bag policy.
All bags are prohibited other than clear vinyl bags no larger than 12″ wide x 12″ height x 6″ deep. Gallon size Ziploc bags and small clutch purses are allowed but you can only have either or. If you are purchasing WWE merchandise inside the arena, the bags they give you are allowed. Non-clear diaper bags are prohibited and so are backpacks.
If you can avoid entraining the stadium without a bag, do it. It will not only speed up your entry since bags are thoroughly checked and inspected upon entrance but will also minimize the risk of being turned away. The stadium will not keep bags for anyone and you would have to go place them back in your vehicle.
