Defining parameters
| Level: | \( N \) | = | \( 538 = 2 \cdot 269 \) |
| Weight: | \( k \) | = | \( 4 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Sturm bound: | \(72360\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(538))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 27403 | 9045 | 18358 |
| Cusp forms | 26867 | 9045 | 17822 |
| Eisenstein series | 536 | 0 | 536 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(538))\)
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 |
|---|---|---|---|---|
| 538.4.a | \(\chi_{538}(1, \cdot)\) | 538.4.a.a | 13 | 1 |
| 538.4.a.b | 15 | |||
| 538.4.a.c | 18 | |||
| 538.4.a.d | 21 | |||
| 538.4.b | \(\chi_{538}(537, \cdot)\) | 538.4.b.a | 68 | 1 |
| 538.4.d | \(\chi_{538}(5, \cdot)\) | n/a | 4422 | 66 |
| 538.4.e | \(\chi_{538}(9, \cdot)\) | n/a | 4488 | 66 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(538))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(538)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(269))\)\(^{\oplus 2}\)