Defining parameters
| Level: | \( N \) | = | \( 8 = 2^{3} \) |
| Weight: | \( k \) | = | \( 10 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(40\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(8))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 21 | 12 | 9 |
| Cusp forms | 15 | 10 | 5 |
| Eisenstein series | 6 | 2 | 4 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)
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 |
|---|---|---|---|---|
| 8.10.a | \(\chi_{8}(1, \cdot)\) | 8.10.a.a | 1 | 1 |
| 8.10.a.b | 1 | |||
| 8.10.b | \(\chi_{8}(5, \cdot)\) | 8.10.b.a | 8 | 1 |
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)