Defining parameters
| Level: | \( N \) | = | \( 10 = 2 \cdot 5 \) |
| Weight: | \( k \) | = | \( 8 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(48\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(10))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 25 | 5 | 20 |
| Cusp forms | 17 | 5 | 12 |
| Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(10))\)
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 |
|---|---|---|---|---|
| 10.8.a | \(\chi_{10}(1, \cdot)\) | 10.8.a.a | 1 | 1 |
| 10.8.b | \(\chi_{10}(9, \cdot)\) | 10.8.b.a | 4 | 1 |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)