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

We calculate the cuspidal class number of a certain quotient curve of the modular curve X-0(M) with M square-free. For each factor r of M, let w(r) denote the Atkin-Lehner type involution of X-0(M). Let M-0 be a, divisor of M, and W-0 the subgroup of the automorphism group of X-0(M) consisting of all w(r) with r dividing M-0. Our object is the quotient X-0(M) by W-0. In this paper, we consider the case where M is odd.