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S Tsuyumine [MR:853217, MR:853222] gives 34 generators for the ring $M_{*}({\rm Sp}(6,\mathbb{Z}))$ of Siegel modular forms of degree 3 with with respect to the full modular group. Tsuyumine also gives a formula for the dimensions of the spaces at each weight.

Miyawaki [MR:1194572] computed enough coefficients in weight 12 and 14 to determine the the Euler factor at the prime 2, and conjectured the Miyawaki lifts.

C. Poor, J. Shurman, and D. S. Yuen [arXiv:1604.07216] computed coefficients coefficients in weights 16, 18, 20, 22, and determined the eigenforms.

Knowl status:
  • Review status: beta
  • Last edited by Andrew Sutherland on 2016-06-30 21:05:16
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