The ring of Siegel modular forms of degree 4 with respect to the full modular group (awaiting review)

The dimensions for degree 4 Siegel modular cusp forms $S_k(\mathrm{Sp}(8,Z))$ for the full modular group for weights $k\le 16$ were proven by C. Poor and D. S. Yuen [MR:2302669]. Poor and Yuen also computed Fourier coefficients and some eigenvalues.

The cusp forms in weights up through 14 are either Duke-Imamoglu-Ikeda lifts or Miyawaki lifts. In weight 16, in addition to these two types of lifts, there are other eigenforms that have been shown by Ibukiyama to instantiate a conjectural lift from vector-valued Siegel modular forms.