Developers write logging statements to generate logs that provide valuable runtime information for debugging and maintenance of software systems. Log level is an important component of a logging statement, which enables developers to control the information to be generated at system runtime. However, due to the complexity of software systems and their runtime behaviors, deciding a proper log level for a logging statement is a challenging task. For example, choosing a higher level (e.g., error) for a trivial event may confuse end users and increase system maintenance overhead, while choosing a lower level (e.g., trace) for a critical event may prevent the important execution information to be conveyed opportunely. In this paper, we tackle the challenge by first conducting a preliminary manual study on the characteristics of log levels. We find that the syntactic context of the logging statement and the message to be logged might be related to the decision of log levels, and log levels that are further apart in order (e.g., trace and error) tend to have more differences in their characteristics. Based on this, we then propose a deep-learning based approach that can leverage the ordinal nature of log levels to make suggestions on choosing log levels, by using the syntactic context and message features of the logging statements extracted from the source code. Through an evaluation on nine large-scale open source projects, we find that: 1) our approach outperforms the state-of-the-art baseline approaches; 2) we can further improve the performance of our approach by enlarging the training data obtained from other systems; 3) our approach also achieves promising results on cross-system suggestions that are even better than the baseline approaches on within-system suggestions. Our study highlights the potentials in suggesting log levels to help developers make informed logging decisions.