The quantum notation used in the "traditional" .par formatted line-by-line lists for each molecule in the HITRAN database was described in detail in the supplementary material of the HITRAN2020 paper . This information is reproduced in the following document, and will be maintained for future updates to the database:
In addition, supplementary XSAMS notation (with more detail) is available for each line if one requests a custom output format to include this information. Details of the XSAMS notation is available on the Virtual Atomic and Molecular Database Consortium (VAMDC)
 I. E. Gordon, L. S. Rothman, R. J. Hargreaves, R. Hashemi, E. V. Karlovets, F. M. Skinner, et al., "The HITRAN2020 molecular spectroscopic database", J. Quant. Spectrosc. Radiat. Transfer 277, 107949 (2022).