Numerical theory nt. Is there a conjectural analogue of Ribet's theorem (Converse's theorem to Herbrand's theorem) for imaginary quadratic fields?

by $ p $ a cousin, let's go $ Cl ( mathbb {Q} ( mu_p)) $ denote the class group the extension of $ mathbb {Q} $ obtained by attaching a primitive $ p $The root of the unit. Associated to a proper form of weight 2 and nebentype, a power of the character of Teichmuller that exhibits a congruence with a series of Eisenstein is his mod. $ p $ Galois representation that is superior triangular. This representation of Galois coincides with a line in its own space in $ Cl ( mathbb {Q} ( mu_p)) otimes mathbb {F_p} $.

It seems natural that anyone who is familiar with this construction of Ribet ask if there are analogs of this result, for example, imaginary quadratic fields? One can attribute representations of superior triangular Galois similar to the data of the group of classes associated to these fields, can have similar conjectural expectations in this case.