Why would it be the Eastern Roman Empire when it didn't even include Rome?
Rome wasn’t even A capital of the late Western Roman Empire.
Yeah, I think they had Ravenna as the capital.
RINO Tom said a capital for a reason. The Roman Empire in the West tried a bunch of more forward-facing capitals first: Milan/Mediolanum because it was so much further north and closer to the frontier, and during the 4th century they even made Trier (Augusta Treverorum) a capital of the West to put the emperor on the front lines. The 5th century move to Ravenna (which is basically an impregnable city in the middle of a swamp that can't be taken without naval superiority) is a humiliating concession that the Imperial capital needs to be hidden away where it cannot be taken.
Speaking of Ravenna, when the Empire took back Italy from the Ostrogoths in the 6th century, it promptly lost most of its gains to the Lombards, but due to Ravenna's defensibility, it held onto it for WAY longer, until the 750s.
Nice map of Europe in 700. You can see the Empire continuing to hold Ravenna and Rome (and Sicily) even though the rest of Italy has fallen to the Lombards.