It is well known that modular forms for a discrete subgroup (formula presented) can be interpreted geometrically as sections of a sheaf or a line bundle over the Riemann surface.
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Choie, Y. J., & Lee, M. H. (2019). Projective structures. In Springer Monographs in Mathematics (pp. 235–249). Springer. https://doi.org/10.1007/978-3-030-29123-5_13
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