  Newform Dedekind sums are a class of crossed homomorphisms that arise from
newform Eisenstein series. We initiate a study of the kernel of these newform
Dedekind sums. Our results can be loosely described as showing that these
kernels are neither "too big" nor "too small." We conclude with an observation
about the Galois action on Dedekind sums that allows for significant
computational efficiency in the numerical calculation of Dedekind sums.
