Tire is losing air but inner tube seems to hold air

I got a flat on my back tire and bought a new innertube. I put it on my bike, filled it up but it lost all air again within minutes. I took the new tube out, pumped it up to find out where the hole is, but I couldn’t find a hole and the tube didn’t lose any air.

I installed the tube again and the tire went flat within minutes. I repeated this process a few times with the same result.

My bike is an E-Bike and I am reluctant to take it to a bike shop because in my area they charge some extra money for E-Bike repairs.