## Dimension table of spaces of degree 2Siegel 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 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 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]

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