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.
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