Algebraic properties of the values of newform Dedekind sums

We study the image of a generalized Dedekind sum relating to the weight zero Eisenstein series $E_{{\chi }_1,{\chi }_2}$. We show that the image is a lattice of full rank inside a number field determined by the characters ${\chi }_1$ and ${\chi }_2$. We also give a generalization of Knopp’s identity for the classical Dedekind sum.