Eisenstein ideal
= Eisenstein ideal
{c}
The Eisenstein ideal in a <modular Hecke algebra> imposes the eigenvalue relations of an Eisenstein series, such as $T_\ell-(1+\ell)$ in an appropriate weight-two trivial-character setting. Congruences modulo this ideal connect <modular forms> and class-field constructions in the <Mazur-Wiles theorem>. Other weights and characters require adjusted eigenvalues.