Dimension table of spaces of degree 2 Siegel modular forms
The table below lists, for each bold value of $k$ in the header, the dimensions of the following subspaces of $M_{k,j}\left(\Gamma_1(2)\right)$ for $j=2$:
- First entry of the respective triple: The full space.
- Second entry: The codimension of the subspace of cusp forms.
- Third entry: The subspace of cusp forms.
More precisely, The triple $[a,b,c]$ in
- row All and in the $k$th column shows the dimension of the full space $M_{k,j}(\Gamma(2))$, of the non cusp forms, and of the cusp forms.
- in row $p$, where $p$ is a partition of $3$, and in the $k$th column shows the multiplicity of the $\Gamma_1(2)$-representation associated to $p$ in the full $\Gamma_1(2)$-module $M_{k,j}(\Gamma(2))$, in the submodule of non cusp forms and of cusp forms. (See below for details.)
| $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ | |
|---|---|---|---|---|---|---|---|
| All | [0, 0, 0] | [0, 0, 0] | [5, 4, 1] | [3, 0, 3] | [10, 4, 6] | [6, 0, 6] | [24, 8, 16] |
| 3 | [0, 0, 0] | [0, 0, 0] | [2, 2, 0] | [0, 0, 0] | [4, 2, 2] | [0, 0, 0] | [9, 4, 5] |
| 21 | [0, 0, 0] | [0, 0, 0] | [3, 2, 1] | [1, 0, 1] | [5, 2, 3] | [3, 0, 3] | [12, 4, 8] |
| 111 | [0, 0, 0] | [0, 0, 0] | [0, 0, 0] | [2, 0, 2] | [1, 0, 1] | [3, 0, 3] | [3, 0, 3] |