Defining parameters
| Level: | \( N \) | = | \( 8026 = 2 \cdot 4013 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Sturm bound: | \(8052084\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8026))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2017033 | 671006 | 1346027 |
| Cusp forms | 2009010 | 671006 | 1338004 |
| Eisenstein series | 8023 | 0 | 8023 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8026))\)
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 |
|---|---|---|---|---|
| 8026.2.a | \(\chi_{8026}(1, \cdot)\) | 8026.2.a.a | 71 | 1 |
| 8026.2.a.b | 81 | |||
| 8026.2.a.c | 86 | |||
| 8026.2.a.d | 96 | |||
| 8026.2.b | \(\chi_{8026}(8025, \cdot)\) | n/a | 334 | 1 |
| 8026.2.d | \(\chi_{8026}(53, \cdot)\) | n/a | 5360 | 16 |
| 8026.2.e | \(\chi_{8026}(831, \cdot)\) | n/a | 5344 | 16 |
| 8026.2.f | \(\chi_{8026}(263, \cdot)\) | n/a | 19430 | 58 |
| 8026.2.h | \(\chi_{8026}(119, \cdot)\) | n/a | 19372 | 58 |
| 8026.2.j | \(\chi_{8026}(7, \cdot)\) | n/a | 310880 | 928 |
| 8026.2.k | \(\chi_{8026}(9, \cdot)\) | n/a | 309952 | 928 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8026))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(8026)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(4013))\)\(^{\oplus 2}\)