Congruences between Siegel modular forms on the level of group cohomology
Vector-valued Siegel modular forms may be found in certain cohomology groups with coefficients lying in an irreducible representation of the symplectic group. Using functoriality in the coefficients, we show that the components of the cohomology are independent of the weight parameter. The meaning of depends on a choice of parabolic subgroup of , giving a particular direction in the change of weight. Our results complement those of Taylor and Tilouine-Urban for the two other possible classes...