Explicit generators of the space of modular forms

Let $S_{\kappa }$ be the space of cusp forms of weight $\kappa$ and level one, and let $S_{\kappa }^{\ast }$ denote its dual space. In this paper, we find explicit spanning subsets of $S_{\kappa }$ consisting of Rankin-Cohen brackets of Eisenstein series and explicit subsets of periods that span $S_{\kappa }^{\ast }$.