Integral Hodge theory and congruences between modular forms
The authors offer a new perspective on the construction of fusion modules between new and old modular forms. They develop the Eckmann-Hodge theory for hermitian local systems over graphs and use it to study integral models of the symmetric power representations of a quaternion algebra over the rationals (Chapter 2). All this is necessary in constructing a module of fusion \(\Phi\) between the automorphic forms of a definite quaternion algebra (Chapter 3, especially Theorem 3.25). Transferring \(\Phi\) to a module of fusion between forms on \(GL(2)\) one obtains a module of fusion for classical modular forms (Corollary 4.11). An application to congruences between modular forms is given (Theorem 4.12).
symmetric power representations of a quaternion algebra
scientific article; zbMATH DE number 878420
scientific article