Aspects of quadratic Chabauty via modular forms

Source abstract

We develop algorithms to construct a basis of de Rham cohomology for modular curves and a matrix representing the Hodge filtration required in the quadratic Chabauty method. We do this without requiring an explicit plane model of the curve and instead compute these objects in terms of modular forms. Our approach works for any modular curve; to demonstrate its efficiency, we implement our method for nonsplit Cartan modular curves.