Hey there, Camelh!
Most probably you are dealing with a faulty battery.
I'd suggest to plug it in again and check if the battery is charging.
Go to the Apple > left side of the menu bar >
> About This Mac
> More Info
> System Report
> Hardware
> Power
Check what does it say about the battery? Capacity, cycle count, condition?
If the condition there says anything else than 'Normal', you have a problem on your hands.
Since the Mac is new, I'd suggest to contact Apple's tech support.
It is still under warranty, so you might have the option to get a replacement!
Hope this helped.
SuperSoph_WD