Eta quotients of level $20$ and weight $1$

Abstract

We find all the eta quotients in the spaces $M_{1}\left(\Gamma_{0}(20), \left(\frac{d}{*}\right)\right)$ with $d = -4, -20$ of modular forms, and we determine their Fourier coefficients, where $\left(\frac{d}{*}\right)$ is the Legendre-Jacobi-Kronecker symbol in the group of Dirichlet characters modulo $20$ with values in the rational field $\mathbb{Q}$.