No, Sparta was not part of the Roman Empire in the way many people might think. While Spartans did come into contact with the Roman Republic, Sparta itself was a significant city-state in ancient Greece long before Rome expanded to become an empire.
Sparta was known for its military prowess and unique social structure, particularly during the 5th century BC. It played a crucial role in the Greco-Persian Wars and later became a dominant power in the Peloponnesian War against Athens.
By the time Rome began to rise to prominence, Sparta had already seen a decline in its influence and power. In 146 BC, the Romans conquered the Greek world and established the province of Achaea, which included Sparta. However, it was not a dominant city within this Roman province. Over time, Sparta transformed and lost much of its former glory and autonomy under Roman rule.
Thus, while Sparta fell under Roman control, it did not function as a significant part of the Roman Empire in the same sense as other territories did, such as those in Gaul or the eastern provinces. It existed more as a local city under Roman authority, rather than as a fully integrated part of the Empire’s political or military framework.