Eta-product $\eta (7\tau {)}^7\mathrm{/}\eta (\tau )$

The Dirichlet series associated to the eta-product $\eta (7\tau {)}^7\mathrm{/}\eta (\tau )$ decomposes uniquely into the difference of two L-functions with Euler products. This expression gives a new proof of the positivity of the Fourier coefficients of the eta-product.