The cuspidal class number formula for certain quotient curves of the modular curve X₀(M) by Atkin-Lehner involutions

Abstract

We calculate the cuspidal class number of a certain quotient curve of the modular curve X₀(M) with M square-free. For each factor r of M, let w_r denote the Atkin-Lehner type involution of X₀(M). Let M₀ be a divisor of M, and W₀ the subgroup of the automorphism group of X₀(M) consisting of all w_r with r dividing M₀. Our object is the quotient of X₀(M) by W₀. In this paper, we consider the case where M is odd.