A splitting into the double cover of SL$$(3,\mathbb {R})$$

Abstract

We provide a formula for the splitting of a congruence subgroup of SL\((3,\mathbb {R})\) into the double cover of SL\((3,\mathbb {R})\) in terms of Plücker coordinates. This new formula is then used to prove that the splitting satisfies a twisted multiplicativity. This formula has applications to the computation of Fourier coefficients of Eisenstein series on the double cover of SL(3) over \(\mathbb {Q}\).