Actually, we don't know that. There's much dispute about the actual composition of the Sanhedrin. We may assume that the head of the Court might have been the High Priest- that would make sense. But, as to the rest of the participants, there's no definite consensus. The Talmudic sources point to the position on the Court to be based on meritocracy.
Here are some verses for consideration.
2Ch 19:8 Moreover in Jerusalem did Jehoshaphat set of the Levites, and of the priests, and of the chief of the fathers of Israel, for the judgment of the LORD, and for controversies, when they returned to Jerusalem.
Lord's matters, vs kings matters......
2Ch 19:11 And, behold, Amariah
the chief priest is over you in all matters of the LORD; and Zebadiah the son of Ishmael, the ruler of the house of Judah, for all the king’s matters: also the Levites shall be officers before you. Deal courageously, and the LORD shall be with the good.
2Ch 30:22 And Hezekiah spake comfortably unto all the Levites that taught the good knowledge of the LORD: and they did eat throughout the feast seven days, offering peace offerings, and making confession to the LORD God of their fathers.
2Ch 35:3 And said unto
the Levites that taught all Israel, which were holy unto the LORD, Put the holy ark in the house which Solomon the son of David king of Israel did build; it shall not be a burden upon your shoulders: serve now the LORD your God, and his people Israel,
Ne 8:7 Also Jeshua, and Bani, and Sherebiah, Jamin, Akkub, Shabbethai, Hodijah, Maaseiah, Kelita, Azariah, Jozabad, Hanan, Pelaiah, and
the Levites, caused the people to understand the law: and the people stood in their place.
Ne 8:9 And Nehemiah, which is the Tirshatha, and
Ezra the priest the scribe, and the Levites that taught the people, said unto all the people, This day is holy unto the LORD your God; mourn not, nor weep. For all the people wept, when they heard the words of the law.
And this...
Heb 7:11 If therefore perfection were by the Levitical priesthood, (
for under it the people received the law,) what further need was there that another priest should rise after the order of Melchisedec, and not be called after the order of Aaron?