It sounds like a 502, which was my first Tek and I still have it stored away. It is a double beam with one timebase common to both beams. It's a little bit smaller than a 545. The vertical amps are built in and use very high quality low noise tubes that audiophooles would kill for. It was intended for biomedical use and the VAs are very sensitive, down to 100 uV/div and the bandwidth varies from 500 KHz down to 100 KHz at maximum sensitivity. I appreciated it at the time when I was working on audio stuff and RTTY modems etc but it's not really practical for other things.
Some decades ago (2 or 3) I had a different dual trace scope but am unsure of the model number. It was the size of the 545 with no separate power unit. It had two vertical channels and time base without any plug-ins as I remember. The bandwidth was modest, meant for medical/physiology use.
It must have been the 502. Maybe I will discover it buried in my long-neglected storage unit.