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 $M_k\left(\Gamma_0(4),\psi_4\right)$:

Odd weights are not yet implemented.

$0$ $2$ $4$ $6$ $8$ $10$ $12$ $14$ $16$ $18$ $20$ $22$ $24$ $26$ $28$ $30$ $32$ $34$ $36$ $38$ $40$
Total 0 0 0 0 0 0 1 4 9 17 29 45 66 93 126 166 214 270 335 410 495

Enter a new range of weights for dimension table:

$k$:     

The ring of Siegel modular forms of degree 2 with respect to $\Gamma_0(4)$ with character

By results of Aoki and Ibukiyama [MR:2130626, 10.1142/S0129167X05002837] , and of Hayashida and Ibukiyama [MR:1840071] , the module $\oplus_k M_{k}(\Gamma_0(4),\psi_4)$ of Siegel modular forms of degree 2 with respect to the group $\Gamma_0(4)$ and character $\psi_4$ is generated by the following functions, which are defined in terms of theta constants:

Note that we write $F(2\Omega)$ to mean "apply $F$ after doubling the input".

The generators $X, X(2\Omega),f_2(2\Omega), K(2\Omega)$ are algebraically independent. Let $B={\Bbb C}[X, X(2\Omega),f_2(2\Omega), K(2\Omega)]$. The module of modular forms with character of even weights only is then give by $$ \oplus_{k=0}^\infty M_{2k}(\Gamma_0(4),\psi_4) = f_{11}(2\Omega)f_{1}(2\Omega)B + Y(2\Omega) B + f_{11}(2\Omega)f_{3}(2\Omega)B, $$ where $f_1=\theta_{0000}^2$ and $f_3=(\theta_{0000}\theta_{0001}\theta_{0011})^2$.