Differential modular forms over totally real fields of integral weights

In this article, we construct a differential modular form of non-zero order and integral weight for compact Shimura curves over totally real fields bigger than Q. The construction uses the theory of lifting ordinary mod p Hilbert modular forms to characteristic 0 as well as the theory of Igusa curve. This is the analogue of the construction of Buium in the case of modular curves parametrizing elliptic curves with level structures.