Sorry, but the only proper definition of the Jews is as a 'people,' a group of
humans that to varying degrees share some similar ethnic and cultural characteristics, but not exclusively. A 'Jew' is therefore a member of the Jewish people, nothing more.
To speak of a Jewish race is incorrect in the commonly understood definition of 'race,' for there were and are Jews of a variety colors and physical types. To speak of Judaism rigidly as a culture or ethnicity, is also difficult, because although there have been common elements preserved through tradition and religion, Jewish communities have for the past 2000 years often assumed the language, dress, and diets of the regions in which they lived. And of course, to define a Jew in strictly religious terms is also incorrect, for there are and have always been Jewish people who practice and adhere to the Jewish religion to varying degrees or none at all. Thus the only proper definition of the Jews is a 'people', and a 'Jew' as a self- or society-defined member of that people.
For a full history, see Jew.