The twelve tribes of Israel were:
Asher
Benjamin
Dan
Ephraim
Gad
Issachar
Judah
Manasseh
Naphtali
Reuben
Simeon
Zebulun
Joseph’s sons were each accounted a “tribe” to honor their father Joseph.
The descendants of Jacob’s son Levi became the Priesthood for Israel, thus while they were a separate tribe, they were not given land and are generally not counted as one of the twelve tribes of Israel.
You are correct about the Levites not getting land. You are incorrect that they are not considered a tribe in their own right. Manasseh is a half-tribe.