Air Carrier flight crew flying a CRJ-200 aircraft reported a GPWS warning during initial approach.

Narrative

Captain was flying; during their approach brief; they briefed the pattern entry altitude. I can not remember the exact altitude they briefed; however their math was incorrect and it was less then the typical 1;500 ft. pattern altitude. I did not catch this. Neither of us noticed on pattern entry. We started to descend further on base; and we both noted how the terrain looked odd. We then got a 'Terrain Pull up' aural message and the Captain turned off the auto pilot and climbed to the correct pattern altitude and continued the approach and made a safe landing. We realized the mistake immediately.The biggest cause was the incorrect math on the pattern entry; which caused us to enter the pattern already low. Contributing factors included me (Pilot Monitoring (PM)) monitoring both CTAF and Center [frequency] because it was uncontrolled; it was a shorter flight; we were looking for traffic around the time we were briefing; TCAS wasn't functioning properly; I didn't catch his mistake in pattern altitude; and neither of us were familiar with the airport.Briefing during a low area of vulnerability so we can both pay more attention to the brief and catch mistakes early; and if its a shorter flight; briefing on the ground prior or asking for a delay vector to make more time.