### Newform Eisenstein Congruences of Local Origin

Linfoot Number Theory Seminar

1st February 2023, 11:00 am – 12:00 pm

Fry Building, Room 2.04

The theory of Eisenstein congruences dates back to Ramanujan’s surprising discovery that the Fourier coefficients of the discriminant function are congruent to the 11th power divisor sum modulo 691. This observation can be explained via the congruence of two modular forms of weight 12 and level 1; the discriminant function and the Eisenstein series, E_{12}. We explore a generalisation of this result to newforms of weight k > 2, squarefree level and non-trivial character. Time permitting, we will discuss what these congruences tell us about the Bloch-Kato conjecture.

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