tao 110cc go kart battery replacement

[1fixitman]

I have a 2016 tao 110cc go kart. I am looking for a battery replacement but the dimensions for the battery box is small. About 4.5 inches Long 2.56 inches wide and height can be 4-6 inches. I was trying to find one on amazon using YTX4L 4AH and all the dimensions are bigger. This battery box is tiny.
There is a diehard 1x4L in the cart that is no good but was looking for cheaper option than advance auto parts for 100$. Has anyone else had the same issue trying to order one. Thank you for your help.