Which window balance do I need?

Thanks for posting. That stamp code is not an identifier; it tells us the strength of the balance. The identity is determined from the attachments on both ends. From what I can see, I believe you have either an S380-27 or S385-27 Channel Balance. The only difference between these two balances is the depth of the bottom nylon shoe, or the measurement from 'heel' to 'toe'. See the diagram below for reference. Compare both balances with your old hardware to see what matches best. In either case for a new stamp option choose 2640.

Comparison of the S378, S380 and S385 balance shoes.