Battery troubles with MBP (early-2011)

My early-2011 MacBook Pro (running Sierra) has been having battery issues. The original battery recently began dying, so I ordered a third-party battery off eBay. I installed the new battery myself. (I've swapped out a number of batteries on MacBooks, so I'm quite confident it is installed correctly.) However, the new battery does not seem to be working properly; it drains very rapidly. I get maybe an hour's use on a full charge, no matter what applications I'm running. It also seems to take much longer to fully charge than it should. Obviously, I suppose, the new battery could be at fault, but I'm concerned because I ran Apple Hardware Test, and the result indicated a battery problem which I'm not certain refers to the actual health of the battery. (By the way, the battery menu bar icon indicates the condition is "normal.") The error code AHT gives me reads as follows:

Alert! Apple Hardware Test has detected an error.

4xxx/4/40000005: ⃟oä "Battery"

Can anyone tell me if this indicates a bad battery, or has something to do with--and forgive me, I don't exactly know how to phrase this--the battery connection or how it interfaces with the computer itself? I guess, in other words, I'm asking if this seems to be a problem with the battery or something more serious.

The reseller is happy to send me a new battery, but only after I return this one, which would be fine but I understand that my MBP will run at a reduced rate if I use it with the power adapter absent a battery. (Can anyone confirm this?)

Any and all help will be appreciated. Thanks in advance!