I have a problem with my first floor toilet, when you flush, an air pocket comes up through the flapper and the water in the tank does not empty all the way out, and the toilet does not flush without me having to plunge it. I have taken an auger to the main floor drain, I have snaked out both first floor and basement toilet. I have taken the toilet off the floor and snaked down through the hole and also changed the wax rings. There is no other backed up drains,(sink or tub). Does anyone have any ideas about this problem it would be greatly appreciated.

Thank You,