In this paper, we investigate cooperative spectrum sensing (CSS) in a cognitive radio network (CRN) where multiple secondary users (SUs) cooperate in order to detect a primary user, which possibly occupies multiple bands simultaneously. Deep cooperative sensing (DCS), which constitutes the first CSS framework based on a convolutional neural network (CNN), is proposed. In DCS, instead of the explicit mathematical modeling of CSS, the strategy for combining the individual sensing results of the SUs is learned autonomously with a CNN using training sensing samples regardless of whether the individual sensing results are quantized or not. Moreover, both spectral and spatial correlation of individual sensing outcomes are taken into account such that an environment-specific CSS is enabled in DCS. Through simulations, we show that the performance of CSS can be greatly improved by the proposed DCS.