On higher congruences between cusp forms and Eisenstein series. (English) Zbl 1355.11043

Naskręcki, Bartosz

Böckle, Gebhard (ed.) et al., Computations with modular forms. Proceedings of a summer school and conference, Heidelberg, Germany, August–September 2011. Cham: Springer (ISBN 978-3-319-03846-9/hbk; 978-3-319-03847-6/ebook). Contributions in Mathematical and Computational Sciences 6, 257-277 (2014).

Summary: The paper contains a numerical study of congruences modulo prime powers between newforms and Eisenstein series at prime levels and with equal weights. We study the upper bound on the exponent of the congruence and formulate several observations based on the results of our computations.
For the entire collection see [Zbl 1283.11007].

MSC:

11F33

Congruences for modular and \(p\)-adic modular forms

Keywords:

Eisenstein series; elliptic curves; \(\lambda\)-adic valuation; congruences