Is it safe for a baby to sleep/live in a completely finished basement??

I am living with my mom right now and she has a basement with a bathroom, 2 bedrooms, and a living room. I have a 4 week old baby and I’m wondering if you think it’s safe to have her down there? It can be quite cold but I have a space heater. I know an unfinished basement can be bad for health but what are your opinions on this?