  The structure of charge density wave states in AV$_3$Sb$_5$ (A = K, Rb, Cs)
kagome superconductors remains elusive, with three possible
$2a\times2a\times2c$ candidates: tri-hexagonal, star-of-David, and their
mixture. In this study, we conducted a systematic first-principles
investigation of the nuclear quadrupole resonance (NQR) and nuclear magnetic
resonance (NMR) spectra for the $2a\times2a\times2c$ CsV$_3$Sb$_5$ structures.
By comparing our simulations with experimental data, we have concluded that the
NQR spectrum indicates the tri-hexagonal structure as the proper structure for
CsV$_3$Sb$_5$ after its charge density wave phase transition. The NMR
calculation results obtained from the tri-hexagonal structure are also
consistent with the experimental data.
