Title: Ramanujan-style congruences for prime level.
Abstract: The prototype of a Ramanujan congruence goes back to Ramanujan (1916) which asserts that the Ramanujan delta function is congruent to the Eisenstein series of weight 12 modulo 691. There are several well-known ways to prove, interpret, and generalize Ramanujan's congruence. For higher weights eigenforms of level 1, Ramanujan-style congruences have been obtained by Datskovsky-Guerzhoy whereas for newforms of prime level by Billerey-Menares and Dummigan-Fretwell. Recently, using the theory of period polynomials, Gaba-Popa (under some technical assumptions) extended these results by determining also the Atkin-Lehner eigenvalue of the newform involved.
In this talk, we refine the result of Gaba-Popa under a mild assumption by using completely different ideas. More precisely, we establish congruences modulo certain primes between a cuspidal newform and an Eisenstein series of weight k and prime level.