The Large Sanhedrin, or the Supreme Court of 71 judges, represents Understanding. Understanding, in turn, is the secret of the Supernal Judgment, as reflected in the name of God “The King of Judgment” which we use between Rosh HaShannah and Yom Kippur. Understanding and Repentance are spiritually synonymous, and these are the days when Understanding rules. The 71 judges in the Sanhedrin reflect the name of God Adonai (יהוה) with its gemetria of 26 plus the deep knowledge represented by the expansion of this name (יוד הא ואו הא), with the gematria of 45, and 26+45=71.
The Smaller Sanhedrin courts of 23 were first consulted on every matter, even that of capital punishment. The requirement for the 23 arises because the 10 are the minimum to acquit, two more are needed to find guilty, which gives 22, and since the court cannot have an even number of judges, they add one more.
However, there is a deep meaning for this number. The name of God usually connected to the quality of Mercy is Adonai (יהוה), and its expansions, for example, the one above (יוד הא ואו הא) have 10 letters. So 10 are needed to acquit. The name of God connected to strict judgment, Elohim (אלהים), has 13 letters in the expansion (אלפ למד הי יוד מם). Thus 23 judges can properly combine the Mercy and the Judgment and arrive at a just result.
Art: Charles Hunt - A Plea For Mercy