What happened to the Roman empire after the death of Constantine?

Two important things happened to the Roman Empire after the death of Constantine. First, it became more Christian and less tolerant, not only persecuting pagans and Jews, but eventually destroying all books that did not further the cause of Christianity. Second, the empire went into serious decline, until the Western Empire ceased even to exist after 476 CE.
40 years later the Western Empire was swallowed up by the Goths and others, but the Eastern Empire lasted another 1,000 years until taken over by the Ottoman Turks.