Below are the dimensions of spaces of vector valued Siegel modular forms with full $\mathrm{Sp}(4, \mathbb{Z})$ level structure.
Featured Examples
$\Upsilon_{20}$: the nonlift of lowest weight
$\Upsilon_{24a}$, $\Upsilon_{24b}$: two rational eigenforms of full level in a two-dimensional space.
Featured Spaces
$M_k(\mathrm{Sp}(4, \mathbb{Z}))$ $M_{k,2}(\mathrm{Sp}(4, \mathbb{Z}))$Dimension Table
k ⟍ j | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 | 26 | 28 | 30 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
10 | 2 | 1 | 1 | 2 | 3 | 3 | 5 | 6 | 7 | 9 | 12 | 12 | 17 | 19 | 22 | 26 |
11 | 0 | 0 | 0 | 1 | 1 | 1 | 4 | 4 | 5 | 8 | 10 | 11 | 16 | 18 | 21 | 27 |
12 | 3 | 0 | 2 | 3 | 4 | 4 | 8 | 7 | 11 | 13 | 16 | 18 | 25 | 25 | 32 | 37 |
13 | 0 | 0 | 0 | 1 | 2 | 2 | 5 | 6 | 8 | 11 | 14 | 16 | 22 | 26 | 30 | 36 |
14 | 2 | 2 | 3 | 4 | 6 | 7 | 10 | 12 | 15 | 19 | 23 | 26 | 33 | 37 | 44 | 51 |
15 | 0 | 0 | 1 | 2 | 4 | 5 | 8 | 10 | 13 | 17 | 22 | 25 | 32 | 37 | 44 | 52 |
16 | 4 | 3 | 4 | 6 | 9 | 9 | 15 | 17 | 21 | 25 | 32 | 35 | 45 | 50 | 58 | 67 |
17 | 0 | 0 | 1 | 3 | 5 | 6 | 11 | 13 | 17 | 23 | 28 | 32 | 42 | 48 | 56 | 67 |
18 | 4 | 3 | 5 | 9 | 10 | 13 | 19 | 21 | 27 | 34 | 39 | 46 | 57 | 63 | 74 | 86 |
19 | 0 | 0 | 2 | 4 | 7 | 9 | 15 | 18 | 23 | 30 | 37 | 43 | 54 | 62 | 73 | 85 |
20 | 5 | 4 | 8 | 10 | 15 | 17 | 24 | 28 | 36 | 42 | 52 | 58 | 72 | 80 | 94 | 107 |