City investigators found Carranza took his wife to see the show using tickets designated for employees of the Department of Education.
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The NYC Conflicts of Interest Board made the ruling on Thursday.
The special tickets cost only $10 as part of a partnership with the education department in 2019.
The board found that "in using this ticket for his wife, the chancellor used his city possession to benefit his wife."
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He has been ordered to pay a fine of $1,000 to the board.
Carranza resigned as chancellor in March. He was replaced by former Bronx Executive Superintendent Meisha Porter.
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