Resumen de Periods of Modular Forms and Imaginary Quadratic Base Change

Mak Trifkovic

• Let f be a classical newform of weight 2 on the upper half-plane H(2), 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 ?E/(v{|D|}?F) is in Q. Here ?F is the unique minimal positive period of F, and ?E 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.