### C4-Extensions of Sn as Galois Groups.

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To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations...

An effective construction of homogeneous linear differential equations of order 2 with Galois group $2{A}_{4},2{S}_{4}$ or $2{A}_{5}$ is presented.

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