Defining parameters
| Level: | \( N \) | = | \( 6 = 2 \cdot 3 \) |
| Weight: | \( k \) | = | \( 12 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(24\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(6))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 13 | 3 | 10 |
| Cusp forms | 9 | 3 | 6 |
| Eisenstein series | 4 | 0 | 4 |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(6))\)
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
| Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
|---|---|---|---|---|
| 6.12.a | \(\chi_{6}(1, \cdot)\) | 6.12.a.a | 1 | 1 |
| 6.12.a.b | 1 | |||
| 6.12.a.c | 1 |
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(6))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_1(6)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)