Position actually doesn't have to be reported, at least for the European implementation of mode s enhanced surveillance. The basic set of informations is call sign, altitude, air/ground status, mode s capability and SI report.
The enhanced part contains quite a bit more information:
Selected altitude, roll angle, true track angle, true track angle rate or true airspeed, ground speed, magnetic heading, IAS/Mach, vertical rate (barometric or baro-inertial).
The big question is though what the ATCO can see, they usually get only a subset of those data sets, the most important ones.