Modular equations for congruence subgroups of genus zero (II)

We present a result that the modular equation of a Hauptmodul for a certain congruence subgroup ΓH(N,t) of genus zero satisfies Kronecker's congruence relation. This generalizes the author's previous result about Γ1(m)⋂Γ0(mN). Furthermore we show that the similar result holds for a certain congruence subgroup Γ of genus zero with [Γ:ΓH(N,t)]=2. Finally we prove a conjecture of Lee and Park, asserting that the modular equation of the continued...