Quantum Chromodynamics, which describe the interactions of quarks and gluons, have been found not to violate global parity symmetry. However, the possibility of local parity violations due to transitions in the vacuum state of QCD is not excluded. The effects of these parity violations could be measured in the hot and dense medium created in the ultrarelativistic heavy ion collisions experiment conducted at the Large Hadron Collider, called a Quark-Gluon Plasma, in which the quarks that compose most of ordinary matter are deconfined. In the strong magnetic fields which permeate the QGP in non-central collisions, parity violation would express itself as a charge asymetry with respect to the reaction plane, a phenomenon called the Chiral Magnetic Effect. The measurements of the charge-dependent correlations in a heavy-ion collisions allows to experimentally probe effects of the CME. These measurements are conducted via the use of the second harmonic two-particle correlator with respect to the reaction plane, $\langle\cos(\phi_{a}+\phi_{b}-2\psi)\rangle$ The background affecting these measurements is the consequence of an interplay of strong anisotropic flow and correlations unrelated to the CME. Correlations with respect to the fourth harmonic, $\langle\cos(2\phi_{a}+2\phi_{b}-4\psi)\rangle$, are insensitive to the CME and can be used to estimate the magnitude of these background effects. In this thesis, we present results from charge-dependent correlations with respect to both the second and fourth harmonic event planes measured in Pb+Pb collisions at $\sqrt{s_{NN}} = 2.76$ TeV at the LHC using data from the ALICE detector. We also present calculations of the ratio of the fourth to second harmonics based on the blast-wave model, which serve as a baseline to understand how these background effects scale between one harmonic and another.