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We give a list of 83 holomorphic eta-quotients of integral weight. For each of them we give a simple closed formula for its Fourier coefficients c (l) where l1m with some fixed m24. The proof involves Wohlfahrt's extension of Hecke operators and a dimension formula for spaces of modular forms of general multiplier system.
Xiaojie Zhu (Sun,) studied this question.