During reaching, the brain may rely on internal models to transform desired sensory outcomes into motor commands. This transformation depends on both the state of the limb and the cues that can identify the context of the movement. How are contextual cues and information about state of the limb combined in the computations of internal models? We considered a reaching task where forces on the hand depended on both the direction of movement (state of the limb) and order of that movement in a predefined sequence (contextual cue). When the cue was available, the motor system formed an internal model that used both serial order and target direction to program motor commands. Assuming that the internal model was formed by a population code through a combination of unknown basis elements, the sensitivity of the bases with respect to state of the limb and contextual cue should dictate how error in one type of movement affected all other movement types. Using a state-space theory, we estimated this generalization function and identified the adaptive system from trial-by-trial changes in performance. The results implied that the basis elements were tuned to direction of movement but output of each basis at its preferred direction was multiplicatively modulated by a weak tuning with respect to the contextual cue. Activity fields that multiplicatively encode diverse sources of information may serve as a general mechanism for a single network to produce context-dependent motor output.