I don't really know about cars but usually it's not the battery it's the car.
How you fix a tail ligth from killing battery
Defective alternator, dead cell in battery, or something is on pulling power from the battery.
A new battery doesn't mean a good battery. The new battery may be defective. Return it and get a new new one.
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i would start by testing the battery , i have seen cases where the battery was good enough to start the vehicle but was causing the alternator to do all the work resulting in premature failure. my f150 went through a brand new ford alternator in 2 months .
Check battery connecters to see if they are tiightly connected. I had that some problem and it was the old battery connecters that where loose. I brought some new connecters and had the mechanic put them on. never had a battery problem even sense.
If the battery is defective get a new battery. If you just left something on and ran it down, charge the battery and keep going.
Only if the old battery is defective
If the battery is running down if it sits for a long period of time then either something is on that is pulling power from the battery or the battery has a dead cell. Check the under hood, glove box, trunk, & interior lights. Also check the brake lights. In rare cases it can be a stuck relay such as a power window relay. If it has a dead cell the only fix is to purchase a new battery. That one dell cell will continually run the battery down.
If you install a new battery & new alternator and the battery runs down overnight then you have something pulling power from the battery. Look for any light on the vehicle that is on or a relay that is stuck.
Buy a new battery or call someone to jump your battery
Get a new battery.