Were the purtians part of the New England colonies?

The Puritans were in no way, Lutheran. The Puritans came from England and were a small, evangelical church that were very pious and shunned anything resembling Catholicism or the Church of England. The Puritans were shunned by the established church in England and came to the American colonies to start a new church. Eventually, they became very arrogant and mistreated the Anglican church from formiing in areas of New England, where the Puritans were dominant. The Lutherans were very similar to the Roman Catholic Church and came from Germany, not England.