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

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