A model of Saturn's internal planetary magnetic field based on data from the Cassini prime mission has been derived. In the absence of a determination of the rotation rate, the model is constrained to be axisymmetric. Non-axisymmetric models for a range of plausible planetary rotation periods have also been derived and we evaluate upper limits on the asymmetry of the internal magnetic field based on those models. We investigate whether a maximum in the non-axisymmetric magnetic field can be identified at a particular rotation rate thus providing insight into the rotation rate of the planet's interior. No such peak can unambiguously be identified. An axisymmetric octupole model is adequate to fit the data and addition of higher order terms does not improve the goodness of fit. The largest value of the dipole tilt obtained from non-axisymmetric models (<0.1°) confirm the high degree of symmetry of Saturn's magnetic field.