  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 of
an integer as a sum of two squares. We deduce a relation between this modular
form and translates of the modular form $\eta(z)^4/\eta(2z)^2$. In the last
section we use our main result to give an elementary proof of an identity by
Victor Kac.
