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Based on Ramanujan's theories of elliptic functions to alternative bases, commutative formal group laws, and supercongruence techniques, including the residue-sum technique, we provide an explicit "Hypergeometric-Modularity" method to obtain modularity results for certain hypergeometric Galois representations. We give a few applications. As a bi-product, we give a collection of eta quotients with multiplicative coefficients, explicit connections between hypergeometric values and periods of modular forms will be obtained.
Allen et al. (Sun,) studied this question.