Symbolic Computation for Rankin-Cohen Differential Algebras: A Case Study

Don Zagier defined a “Rankin-Cohen algebra”, motivated by the study of differential operators that send modular forms to modular forms. We devised an algorithm that computes the result of the differentiation given by the modular forms that correspond to higher-order Wronskians over Klein’s quartic curve, which are modular forms of arbitrarily high degree canonically attached to the curve; this tool is potentially useful for finding commutative rings of differential operators.