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.

中文翻译：

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化粪池配分函数的算术性质

同余和相关恒等式是为一组彩色和加权分区函数导出的，其生成函数生成七级整数权重模形式的分级代数。这项工作确定了一种通用策略，用于在级别的主要同余子组上识别和证明模形式的身份和相关同余7. Ramanujan 的分区同余模7作为用于证明模块化水平形式的新全等过程的原型 7.