Constantine's effect on ancient Greece adn Rome is limited by the fact that he lived at almost the end of the ancient period. "Ancient" only goes to about AD 600, while it stretches back to the early bronze age (ca 1400 BC) for its beginning. Constantine lived in the fourth century AD.

However his influence on the last two and a half centuries of the ancient world are profound for two reasons. First, he moved the Imperial capitol to Constantinople. This left Rome as a provincial backwater and allowed the Franks to create their own Roman Empire. Some of our modern royal families today can trace their ancestry back to the early Frankish Holy Roman Emperors.

Second, he endorsed Christianity. And the particular brand of Christianity that he chose was his mother's obscure sect of "historists". Helen's sect believed that Jesus was an actual historical character who lived and breathed as a human man walking around sometime before Hadrian obliterated Jerusalem. Pushing this minority sect required official Christians to adopt several absurdities such as the trinity. The logical contradiction that a god can be three people while simultaneously being one person got it's start from Helen's tiny sect of Christianity. The absurdity of Jesus being wholly human and simultaneously wholly divine "without mixture or conflict" led to actual murder. By the end of the fourth century Christians were actually killing each other over words like "homoousion" and "homoiousion".

As if God cares whether Jesus was "one substance with the father" or "likeness of being with the father". "Homoousion" literally means "same as", while "homoiousion" literally means "similar to". What an absurd thing to kill someone for. Constantine's influence started the killing and eventually led to medieval executions like Giordano Bruno and John Hus and Joan of Arc. The definition of "heresy" as a crime is not inherent in any form of Christianity, it comes from politics. This is the direct influence of Constantine who first politicized Christianity.

The Biblical view of heresy is "If a man is a heretic, after the first and second admonition reject him." That would be shunning. The political view of heresy is: it's a crime against the state, execute him.