Following a joint work with Sara Arias-de-Reyna and François Legrand, we present a new kind of families of modular forms. They come from representations of the absolute Galois group of rational function fields over `$\mathbb{Q}$`

. As a motivation and illustration, we discuss in some details one example: an infinite Galois family of Katz modular forms of weight one in characteristic `$7$`

, all members of which are non-liftable. This may be surprising because non-liftability is a feature that one might expect to occur only occasionally.

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Last updated: 23 Feb 2024