Abstract: Ramanujan made a series of influential conjectures in his 1916 paper &Quotron some arithmetical functions & quot; on what is now called the Ramanujan tau function. In the same paper he also proved a notable congruence mod 691 for the Ramanujan tau function. The existence of such congruences opened the door for many modern developments in the theory of modular forms. For newforms of prime level, some partial results about the existence of such congruences are known. In this talk, we discuss and refine some of those results.
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