Defining parameters
| Level: | \( N \) | = | \( 8031 = 3 \cdot 2677 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 12 \) | ||
| Sturm bound: | \(9555104\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8031))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2394128 | 1794257 | 599871 |
| Cusp forms | 2383425 | 1788905 | 594520 |
| Eisenstein series | 10703 | 5352 | 5351 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8031))\)
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 |
|---|---|---|---|---|
| 8031.2.a | \(\chi_{8031}(1, \cdot)\) | 8031.2.a.a | 92 | 1 |
| 8031.2.a.b | 102 | |||
| 8031.2.a.c | 121 | |||
| 8031.2.a.d | 132 | |||
| 8031.2.b | \(\chi_{8031}(5353, \cdot)\) | n/a | 446 | 1 |
| 8031.2.e | \(\chi_{8031}(1033, \cdot)\) | n/a | 894 | 2 |
| 8031.2.f | \(\chi_{8031}(3227, \cdot)\) | n/a | 1780 | 2 |
| 8031.2.j | \(\chi_{8031}(4321, \cdot)\) | n/a | 890 | 2 |
| 8031.2.l | \(\chi_{8031}(626, \cdot)\) | n/a | 3564 | 4 |
| 8031.2.m | \(\chi_{8031}(10, \cdot)\) | n/a | 99456 | 222 |
| 8031.2.p | \(\chi_{8031}(64, \cdot)\) | n/a | 99012 | 222 |
| 8031.2.q | \(\chi_{8031}(16, \cdot)\) | n/a | 198468 | 444 |
| 8031.2.s | \(\chi_{8031}(8, \cdot)\) | n/a | 395160 | 444 |
| 8031.2.t | \(\chi_{8031}(4, \cdot)\) | n/a | 197580 | 444 |
| 8031.2.w | \(\chi_{8031}(2, \cdot)\) | n/a | 791208 | 888 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8031))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(8031)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(2677))\)\(^{\oplus 2}\)