40 amp service

I did an inspection for a coop apartment which is approximately 50 years old. There is a sub panel in the apartment with a 40 amp main breaker, the panel appears to be recently upgraded but not the service feed (they just added a new panel and used the old panel as junction box). The apartment is a 3 bedroom, approximately 1100 sf. There are no electric appliances or heating systems. Heat is supplied by a main boiler for the building. Would this 40 amp service be considered adequate in this situation?

The only real way to know is by doing a load calculation. Since the existing sub-panel was 40 amps and has been that way for 50 years a load calc is probably not needed.

Yes, a calculation of the loads connected and served would be required, but that that is well beyond the SOP for home inspections. You could, however, mention that such a calcuation might be appropriate.