Christianity was the state religion, but what proportion of people were Christians? What other religions were popular at the time and how were they treated by the Empire?

Did some ethnic groups and regions have notably different religious demographics?

What divisions were there among Christians at the time? Was there already a split between Catholic and Orthodox churches?

What kind of religious officials were there? Were priests of the old Roman gods allowed to continue worship? How about other religions?

Were there monasteries and nunneries at that time?

Were there mystery cults and similar mystical organisations?

And on a slightly related note... what kind of mystical or magical beliefs did people have? Was belief in witches, demons, etc. widespread? Did Christians believe that pagans had magic powers and vice versa?