Congruences and related identities are derived for a set of colored and weighted partition functions whose generating functions generate the graded algebra of integer weight modular forms of level seven. The work determines a general strategy for identifying and proving identities and associated congruences for modular forms on the principal congruence subgroup of level 7. Ramanujan's partition congruence modulo 7 serves as a prototype for the process used to prove new congruences for modular forms of level 7.
Huber, T., Huerta, M., & Mayes, N. (2021). Arithmetic properties of septic partition functions. International Journal of Number Theory. https://doi.org/10.1142/S179304212040031X
International Journal of Number Theory
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