Eta-product $\eta(7\tau)^7/\eta(\tau)$
  The Dirichlet series associated to the eta-product $\eta(7\tau)^7/\eta(\tau)$ 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. 
Kyoji Saito