Resumen de Factoring newparts of Jacobians of certain modular curves

M. Ram Murty, Kaneenika Sinha

• We prove a conjecture of Yamauchi which states that the level for which the new part of is -isogenous to a product of elliptic curves is bounded. We also state and partially prove a higher-dimensional analogue of Yamauchi's conjecture. In order to prove the above results, we derive a formula for the trace of Hecke operators acting on spaces of newforms of weight and level We use this trace formula to study the equidistribution of eigenvalues of Hecke operators on these spaces. For any we estimate the number of normalized newforms of fixed weight and level, whose Fourier coefficients generate a number field of degree less than or equal to