Luminosity dependence of the multiple cyclotron lines in 4U 0115$+$63

The Be X-ray binary 4U 0115$+$63 underwent a giant outburst in 2023 with the X-ray luminosity of the source reaching 10$^{38}$ erg s$^{-1}$. During the outburst, two target of opportunity observations were made with \textit{NuSTAR}. The main goal of this work is to model the multiple cyclotron scattering features (CRSFs) present in 4U 0115$+$63 and study their dependence on the luminosity of the source. The 3$-$79 keV broadband X-ray coverage of \textit{NuSTAR} allowed us to properly model the continuum and investigate the nature of the multiple cyclotron resonance scattering features present in the source spectrum. We used the epoch-folding technique to find the pulsation from the source and also studied the changes in the cyclotron line energy with an order of magnitude variation in the source luminosity. We detected five cyclotron lines during the 2023 outburst near 12, 16, 24, 34, and 47 keV. The $\sim$16 keV cyclotron line cannot be harmonically related to the other cyclotron lines at $\sim$12 keV and $\sim$24 keV. This indicates the presence of two fundamental lines in the spectrum of 4U 0115$+$63 at 12 keV and 16 keV. With the inclusion of the two latest \textit{NuSTAR} observations, we have expanded the data set of the CRSF line center to encompass a broad range of luminosity. This enables us to comprehensively investigate the relationship between the centroid energy of the cyclotron lines and luminosity. The CRSF line center shows no anticorrelation with luminosity, unlike previously reported. Instead, a weak positive correlation is found in four out of the five detected cyclotron lines of 4U 0115$+$63. The luminosity variation of the two fundamental CRSFs could be well explained with the prediction from the collisionless shock model.