An Explicit Cubic Ramanujan--Sato Series for $1/π$ on $Γ_0(2)^+$ at $D=-163$

Abstract

An explicit cubic Ramanujan--Sato formula for $1/π$ on $Γ_0(2)^+$ at $D=-163$ is presented. The construction produces a very small cubic CM parameter, giving about $15.01$ decimal digits of geometric contraction per term. This is slightly sharper than the classical Chudnovsky contraction, but the coefficients lie in a cubic algebraic field.