Defining parameters
| Level: | \( N \) | = | \( 8013 = 3 \cdot 2671 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 16 \) | ||
| Sturm bound: | \(9512320\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8013))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2383420 | 1786229 | 597191 |
| Cusp forms | 2372741 | 1780889 | 591852 |
| Eisenstein series | 10679 | 5340 | 5339 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8013))\)
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 |
|---|---|---|---|---|
| 8013.2.a | \(\chi_{8013}(1, \cdot)\) | 8013.2.a.a | 94 | 1 |
| 8013.2.a.b | 106 | |||
| 8013.2.a.c | 116 | |||
| 8013.2.a.d | 129 | |||
| 8013.2.b | \(\chi_{8013}(8012, \cdot)\) | n/a | 888 | 1 |
| 8013.2.e | \(\chi_{8013}(544, \cdot)\) | n/a | 890 | 2 |
| 8013.2.f | \(\chi_{8013}(2575, \cdot)\) | n/a | 1784 | 4 |
| 8013.2.h | \(\chi_{8013}(545, \cdot)\) | n/a | 1778 | 2 |
| 8013.2.l | \(\chi_{8013}(473, \cdot)\) | n/a | 3552 | 4 |
| 8013.2.m | \(\chi_{8013}(37, \cdot)\) | n/a | 3560 | 8 |
| 8013.2.o | \(\chi_{8013}(881, \cdot)\) | n/a | 7112 | 8 |
| 8013.2.q | \(\chi_{8013}(490, \cdot)\) | n/a | 39248 | 88 |
| 8013.2.t | \(\chi_{8013}(104, \cdot)\) | n/a | 78144 | 88 |
| 8013.2.u | \(\chi_{8013}(40, \cdot)\) | n/a | 78320 | 176 |
| 8013.2.v | \(\chi_{8013}(4, \cdot)\) | n/a | 156992 | 352 |
| 8013.2.x | \(\chi_{8013}(62, \cdot)\) | n/a | 156464 | 176 |
| 8013.2.z | \(\chi_{8013}(11, \cdot)\) | n/a | 312576 | 352 |
| 8013.2.bc | \(\chi_{8013}(10, \cdot)\) | n/a | 313280 | 704 |
| 8013.2.be | \(\chi_{8013}(14, \cdot)\) | n/a | 625856 | 704 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8013))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(8013)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(2671))\)\(^{\oplus 2}\)