  The chiral magnetic effect (CME) induces an electric charge separation in a
chiral medium along the magnetic field that is mostly produced by spectator
protons in heavy-ion collisions. The experimental searches for the CME, based
on the charge-dependent angular correlations ($\gamma$), however, have remained
inconclusive, because the non-CME background contributions are not well
understood. Experimentally, the $\gamma$ correlators have been measured with
respect to the second-order ($\Psi_{2}$) and the third-order ($\Psi_{3}$)
symmetry planes, defined as $\gamma_{112}$ and $\gamma_{123}$, respectively.
The expectation was that with a proper normalization, $\gamma_{123}$ would
provide a data-driven estimate for the background contributions in
$\gamma_{112}$. In this work, we calculate different harmonics of the $\gamma$
correlators using a charge-conserving version of a multiphase transport (AMPT)
model to examine the validity of the said assumption. We find that the
pure-background AMPT simulations do not yield an equality in the normalized
$\gamma_{112}$ and $\gamma_{123}$, quantified by $\kappa_{112}$ and
$\kappa_{123}$, respectively. Furthermore, we test another correlator,
$\gamma_{132}$, within AMPT, and discuss the relation between different
$\gamma$ correlators.
