Defining parameters
| Level: | \( N \) | = | \( 538 = 2 \cdot 269 \) |
| Weight: | \( k \) | = | \( 6 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Sturm bound: | \(108540\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(538))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 45493 | 15075 | 30418 |
| Cusp forms | 44957 | 15075 | 29882 |
| Eisenstein series | 536 | 0 | 536 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(538))\)
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 |
|---|---|---|---|---|
| 538.6.a | \(\chi_{538}(1, \cdot)\) | 538.6.a.a | 24 | 1 |
| 538.6.a.b | 27 | |||
| 538.6.a.c | 30 | |||
| 538.6.a.d | 32 | |||
| 538.6.b | \(\chi_{538}(537, \cdot)\) | n/a | 112 | 1 |
| 538.6.d | \(\chi_{538}(5, \cdot)\) | n/a | 7458 | 66 |
| 538.6.e | \(\chi_{538}(9, \cdot)\) | n/a | 7392 | 66 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(538))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(538)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(269))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(538))\)\(^{\oplus 1}\)