Defining parameters
| Level: | \( N \) | = | \( 8011 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 12 \) | ||
| Sturm bound: | \(10696020\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8011))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2678010 | 2678010 | 0 |
| Cusp forms | 2670001 | 2670001 | 0 |
| Eisenstein series | 8009 | 8009 | 0 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8011))\)
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 |
|---|---|---|---|---|
| 8011.2.a | \(\chi_{8011}(1, \cdot)\) | 8011.2.a.a | 309 | 1 |
| 8011.2.a.b | 358 | |||
| 8011.2.c | \(\chi_{8011}(89, \cdot)\) | n/a | 1332 | 2 |
| 8011.2.d | \(\chi_{8011}(930, \cdot)\) | n/a | 2664 | 4 |
| 8011.2.f | \(\chi_{8011}(1972, \cdot)\) | n/a | 4002 | 6 |
| 8011.2.h | \(\chi_{8011}(501, \cdot)\) | n/a | 5328 | 8 |
| 8011.2.k | \(\chi_{8011}(52, \cdot)\) | n/a | 16008 | 24 |
| 8011.2.l | \(\chi_{8011}(6, \cdot)\) | n/a | 58608 | 88 |
| 8011.2.o | \(\chi_{8011}(22, \cdot)\) | n/a | 117216 | 176 |
| 8011.2.p | \(\chi_{8011}(5, \cdot)\) | n/a | 234432 | 352 |
| 8011.2.r | \(\chi_{8011}(19, \cdot)\) | n/a | 352176 | 528 |
| 8011.2.t | \(\chi_{8011}(4, \cdot)\) | n/a | 468864 | 704 |
| 8011.2.w | \(\chi_{8011}(7, \cdot)\) | n/a | 1408704 | 2112 |
"n/a" means that newforms for that character have not been added to the database yet