Klein forms are used to construct generators for the graded algebra of modular forms of level 7. Dissection formulas for the series imply Ramanujan type congruences modulo powers of 7 for a family of generating functions that subsume the counting function for 7-core partitions. The broad class of arithmetic functions considered here enumerate colored partitions by weights determined by parts modulo 7. The method is a prototype for similar analysis of modular forms of level 7 and at other prime levels. As an example of the utility of the dissection method, the paper concludes with a derivation of novel congruences for the number of representations by x^2+xy+2y^2 in exactly k ways.
Huber, T., & Ye, D. (2020). Ramanujan type congruences for quotients of level 7 Klein forms. Journal of Number Theory. https://doi.org/10.1016/j.jnt.2020.11.003
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Journal of Number Theory