You must have typed the model number from the sticker under the hood incorrectly, as the one you typed that was stamped into the transmission looks correct, BA213C instead of BA231C.
BA213C is a 2600 general purpose ag chassis tractor with a diesel engine, live PTO and 8 speed transmission.
BA231C would be a general purpose ag chassis with a LPG (propane) engine, no PTO and an 8 speed, which would be a less common configuration, although it is possible.
The Unit number is also referred to as the production code, which tells you exactly when it was built. 7F28B says it rolled off the assembly line on June 28, 1977 during the day shift.
The tractor number is also called the serial number. As we discussed earlier, C545985 is a 1977 serial number, which agrees with the Unit number above.
All of the other numbers on the sticker under the hood are production codes of the individual component:
Engine 7E17A - May 17, 1977, midnight shift
Trans 7E26C - May 26, 1977, afternoon shift
Hyd pump 7E24B - May 24, 1977, day shift
Rear Axle 7E31B - May 31, 1977, day shift
Hyd Lift 7E17A - May 17, 1977 midnight shift.