Four weeks ago I contacted the department of the University to ask whether there are PhD positions open. They emailed me some questions I needed to fill in and said that they will review my application and let me know if they have something available for me as soon as possible. After two weeks, I sent a follow-up email asking if there was already some news about my application, but they didn't respond.
Now, two weeks after that follow-up email, I still haven't heard anything. Is it okay to send a second follow-up email? How should I formulate it? I don't want to seem annoying and intrusive. On the one hand, I'm willing to be patient as I really want to pursue a PhD at that faculty, but on the other hand, if they don't offer me a position, I need to start looking for other positions as soon as possible.