Waiting time for editor's decision
After six weeks you can probably ask, but don't ask repeatedly. Just explain that the paper is important to you as a component of your dissertation. You don't need a long explanation or a plea for exceptional treatment. 

Depending on the journal, six weeks may be an instant in time. But it is long enough that it is reasonable to ask. If they are overly busy, however, your question may take a while to answer.