My hybrid bike recently got a piece of glass through my rear tire and innertube.

I bought both a new tire and innertube (700x35c schrader).

I filled up both tires to 65psi. A week later the front tire had 57 psi but the rear tire was at 30. The same thing has been happening for a couple of weeks now.

What can cause this? Did I just cause a small hole while installing the innertube? Is the solution to just replace the innertube again and hope it doesn't happen in the future?