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Predicting the next visited location of an individual is a key problem in human mobility analysis, as it is required for the personalization and optimization of sustainable transport options. Here, we propose a transformer decoder-based neural network to predict the next location an individual will visit based on historical locations, time, and travel modes, which are behaviour dimensions often overlooked in previous work. In particular, the prediction of the next travel mode is designed as an auxiliary task to help guide the network's learning. For evaluation, we apply this approach to two large-scale and long-term GPS tracking datasets involving more than 600 individuals. Our experiments show that the proposed method significantly outperforms other state-of-the-art next location prediction methods by a large margin (8.05% and 5.60% relative increase in F1-score for the two datasets, respectively). We conduct an extensive ablation study that quantifies the influence of considering temporal features, travel mode information, and the auxiliary task on the prediction results. Moreover, we experimentally determine the performance upper bound when including the next mode prediction in our model. Finally, our analysis indicates that the performance of location prediction varies significantly with the chosen next travel mode by the individual. These results show potential for a more systematic consideration of additional dimensions of travel behaviour in human mobility prediction tasks. The source code of our model and experiments is available at https://github.com/mie-lab/location-mode-prediction.