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 $M_{k,j}\left(\Gamma_0(2)\right)$ for $j=2$:

$4$ $5$ $6$ $7$ $8$ $9$ $10$ $11$ $12$ $13$ $14$ $15$ $16$ $17$ $18$ $19$ $20$ $21$ $22$ $23$ $24$
Total 0 0 2 0 4 0 9 1 13 3 22 6 30 10 43 17 56 24 75 35 93
Non cusp 0 0 2 0 2 0 4 0 4 0 6 0 6 0 8 0 8 0 10 0 10
Cusp 0 0 0 0 2 0 5 1 9 3 16 6 24 10 35 17 48 24 65 35 83

Enter a new range of weights for dimension table:

$k$:      $j$:     

The ring of Siegel modular forms of degree 2 for $\Gamma_0(2)$

By a result of Tomoyoshi Ibukiyama [MR:1082834, 10.1142/S0129167X9100003X] , the ring of Siegel modular forms of degree 2 with respect to the group $\Gamma_0(2)$ is generated by the following five generators, which are specified in terms of theta constants.

The generators $X, Y, Z, K$ are algebraically independent. The ring of modular forms is

$$M(\Gamma_0(2)) = \C[X,Y,Z,K] + \chi_{19}\,\C[X,Y,Z,K].$$