Network slicing is increasingly used to partition network infrastructure between different mobile services. Precise service-wise mobile traffic forecasting becomes essential in this context, as mobile operators seek to pre-allocate resources to each slice in advance, to meet the distinct requirements of individual services. This paper attacks the problem of multi-service mobile traffic forecasting using a sequence-to-sequence (S2S) learning paradigm and convolutional long short-term memories (ConvLSTMs). The proposed architecture is designed so as to effectively extract complex spatiotemporal features of mobile network traffic and predict with high accuracy the future demands for individual services at city scale. We conduct experiments on a mobile traffic dataset collected in a large European metropolis, demonstrating that the proposed S2S-ConvLSTM can forecast the mobile traffic volume produced by tens of different services in advance of up to one hour, by just using measurements taken during the past hour. In particular, our solution achieves mean absolute errors (MAE) at antenna level that are below 13KBps, outperforming other deep learning approaches by up to 31.2%.