  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.
