In this paper, we propose a novel approach for agent motion prediction in cluttered environments. One of the main challenges in predicting agent motion is accounting for location and context-specific information. Our main contribution is the concept of learning context maps to improve the prediction task. Context maps are a set of location-specific latent maps that are trained alongside the predictor. Thus, the proposed maps are capable of capturing location context beyond visual context cues (e.g. usual average speeds and typical trajectories) or predefined map primitives (such as lanes and stop lines). We pose context map learning as a multi-task training problem and describe our map model and its incorporation into a state-of-the-art trajectory predictor. In extensive experiments, it is shown that use of learned maps can significantly improve predictor accuracy. Furthermore, the performance can be additionally boosted by providing partial knowledge of map semantics.