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We compute the Fourier coefficients of the weight one modular form$\eta(z)\eta(2z)\eta(3z)/\eta(6z)$ in terms of the number of representations ofan integer as a sum of two squares. We deduce a relation between this modularform and translates of the modular form $\eta(z)^4/\eta(2z)^2$. In the lastsection we use our main result to give an elementary proof of an identity byVictor Kac.

The Fourier expansion of \eta(z)\eta(2z)\eta(3z)/\eta(6z)