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We state and prove an identity which represents the most general eta-productsof weight 1 by binary quadratic forms. We discuss the utility of binaryquadratic forms in finding a multiplicative completion for certaineta-quotients. We then derive explicit formulas for the Fourier coefficients ofcertain eta-quotients of weight 1 and level 47, 71, 135,648 1024, and 1872.

Binary Quadratic forms and the Fourier coefficients of certain weight 1 eta-quotients