The knowledge of tire-rim interface loadings is crucial to design aircraft wheels. A parameterization of these loadings is proposed using model reduction techniques. The static eigenmodes of the wheel stiffness matrix that is condensed at the tire-rim interface provide a suited hierarchy of displacement or loading modes that can be sorted according to their elastic energy. A truncation of this series at a chosen order is performed to approximate any load applied to the rim. The use of cyclic symmetry is shown to lead to an efficient numerical scheme to compute these modes. This parameterization does not involve the tire modeling, which is beyond the control of aircraft wheel manufacturers. The reduced basis composed of the major eigenmodes is shown to be more compact and robust than other parameterizations based on arbitrary shape functions or tire models and will be further used for inverse identifications of tire-rim loadings. Moreover, this approach is generic and offers a convenient and efficient framework for arbitrary loadings.