Class-Number-One Cubic Fricke Companions on $Γ_0(2)^+$ and an Exact Chudnovsky Bridge

Abstract

A structural classification-and-bridge result is proved for RS series on \(Γ_0(2)^+\). Among the fundamental Heegner discriminants with \(h(D)=1\), the irreducibly cubic Fricke-cusp companions occur exactly for \[ D=-11,-19,-43,-67,-163. \] The proof gives an explicit bridge between \(z=1728/j\) and \(X=256t/(t+64)^2\), a hypergeometric gauge identity, and a CM interpretation of the fibre. For \(D=-163\), the cubic Fricke RS series is the exact level-two transport of the Chudnovsky linear form.