Why a new 12v battery would fail that quickly is hard to say. It certainly shouldn't.
First question I'd have is the source where you purchased the battery. Online? A local shop? And if it was local, was it a place that specializes in automotive parts? Who installed it?
All that relates to the integrity of the (presumably) new battery you bought. Not everything described as "new" actually is.
Bottom line is you need to have the battery load tested by someone you can trust. I'd think a failing 3-week old battery would fall under warranty.