  The main result of this article states that the Galois representation
attached to a Hilbert modular eigenform defined over F_p^bar of parallel weight
1 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 1. The proof is based on the observation that parallel weight 1
forms in characteristic p embed into the ordinary part of parallel weight p
forms in two different ways per prime dividing p, namely via `partial'
Frobenius operators.
