The answer to this question depends on which text you read and whom you ask. Until recently, NT scholars stressed the uniqueness of Jesus and the novel character of his message but recently, more emphasis has been laid on his Jewish background. There is no doubt that Jesus was born a Jew, debated topics central to many contemporary Jews (kingdom of heaven, social justice) and died a Jew. The same may be said of his early followers. Note how the women discover the empty grave on the third day—after Shabbat.
For more on this see Paula Frederiksen’s immensely readable From Jesus to Christ (2000).