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Topics on modular Galois representations modulo prime powers. (English) Zbl 1426.11046
Böckle, Gebhard (ed.) et al., Algorithmic and experimental methods in algebra, geometry, and number theory. Cham: Springer. 741-763 (2017).
Summary: This article surveys modularity, level raising and level lowering questions for two-dimensional representations modulo prime powers of the absolute Galois group of the rational numbers. It contributes some new results and describes algorithms and a database of modular forms orbits and higher congruences.
For the entire collection see [Zbl 1394.14002].

MSC:
11F33 Congruences for modular and \(p\)-adic modular forms
11F80 Galois representations
Software:
ArtinAlgebras; Magma
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References:
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