Cuspidal subgroups associated with non-rational Eisenstein maximal ideals

Abstract

In this paper, we are interested in the generalization of Ramanujan-like Eisenstein congruences (congruences between cusp forms and Eisenstein series) for congruence subgroups of the form with . We determine the possible primes that can produce Eisenstein congruences. We provide several examples of Eisenstein congruences to substantiate our method. Ribet conjectured ([38 p. 360]) about these congruences for the square-free level N. Yoo proved the conjecture. For general N, Yoo proved a generalization of the conjecture, under some hypotheses, provided that those ideals are rational. We show that the generalization of Ribet’s conjecture for certain non-square-free levels N is true even for non-rational Eisenstein maximal ideals.