Congruences of local origin and automorphic induction

We explore the possibilities for Galois representation [Formula: see text] attached to a weight-one newform be residually reducible, i.e. Hecke eigenvalues congruent those of Eisenstein series. A special role is played by series level text], where quadratic character associated with an imaginary field discriminant respect which dihedral type. prove congruences, modulus divides either class number or (for prime text]), and in first case, (according as respectively) second. also analogous congruences are replaced its twist Siegel cusp form genus paramodular level, induced some sense from Hilbert modular form.