Twisted Traces of Modular Functions on Hyperbolic 3-Space

We compute analogues of twisted traces of CM values of harmonic modular functions on hyperbolic 3-space and show that they are essentially given by Fourier coefficients of the j-invariant. From this we deduce that the twisted traces of these harmonic modular functions are integers. Additionally, we compute the twisted traces of Eisenstein series on hyperbolic 3-space in terms of Dirichlet L-functions and divisor sums. © 2025 Elsevier Inc.