The main result of this article states that the Galois representation attached to a Hilbert modular eigenform over F_p^bar of parallel weight one and level prime to p is unramified above p. This includes the important case of eigenforms that do not lift to Hilbert modular forms in characteristic 0 of parallel weight one. The proof is based on the observation that parallel weight one forms in characteristic p embed into the ordinary part of parallel weight p in two different ways per place above p, namely via `partial' Frobenius operators. These are defined in the article along with and based on Hecke operators T_P for P dividing p. The theorem is deduced from known local properties of the Galois representation attached to ordinary eigenforms in characteristic 0.
Last modification: 3 July 2017.