Periods of Modular Forms and Imaginary Quadratic Base Change

Abstract

AbstractLet f be a classical newform of weight 2 on the upper half-plane , E the corresponding strong Weil curve, K a class number one imaginary quadratic field, and F the base change of f to K. Under a mild hypothesis on the pair (f, K), we prove that the period ratio is in ℚ. Here ΩF is the unique minimal positive period of F, and ΩE the area of E(ℂ). The claim is a specialization to base change forms of a conjecture proposed and numerically verified by Cremona and Whitley.