  Inspired by the work of G. Harder (\cite{HaICM}, \cite{HaLNM}, \cite{HaMM})
we construct via the motive of a Hilbert modular surface an extension of a Tate
motive by a Dirichlet motive. We compute the realisation classes and indicate
how this is linked to the Hodge-1-motive of the Hilbert modular surface.
