Congruence-class Eisenstein series ($G_k^{(x,y)}$)

For $k>2$ and $(x,y)\in (\mathbb{Z}/N\mathbb{Z}{)}^2$,is a modular form of weight $k$ for the principal congruence subgroup $\Gamma (N)$. Right multiplication of $(x,y)$ by $\gamma \in S{L}_2(\mathbb{Z})$ describes its slash transformation.