Cooperative beamforming across access points (APs) and fronthaul quantization strategies are essential for cloud radio access network (C-RAN) systems. The nonconvexity of the C-RAN optimization problems, which is stemmed from per-AP power and fronthaul capacity constraints, requires high computational complexity for executing iterative algorithms. To resolve this issue, we investigate a deep learning approach where the optimization module is replaced with a well-trained deep neural network (DNN). An efficient learning solution is proposed which constructs a DNN to produce a low-dimensional representation of optimal beamforming and quantization strategies. Numerical results validate the advantages of the proposed learning solution.