I kindly would like to ask you the following- I am refering to page 175 in the Book by Gelfand, Graev, Shapiro, etc, on "Automorphic forms ..."

My question to which I would kindly ask you to answer me is : Are there unitary representations of SL(2, Q_P) of type I (that is with spherical functions) that are not in the continuous series. Gelfand is ambiguous in the text by saying that he will give examples of such class 1 unitary representations in the continuous series. If there other type I unitary reps, in which series are they (the discrete series perhaps?).

What would be the trace formula for this class 1, non-principal series?