  Traces of singular moduli can be approximated by exponential sums of
quadratic irrationals. Recently Andersen and Duke used theory of Maass forms to
estimate generalized twisted traces with power-saving error bounds. We
establish an asymptotic formula with effective error bounds for such traces.
Our methods depend on an explicit bound for sums of Kloosterman sums on
$\Gamma_0(4)$.
