Defining parameters
| Level: | \( N \) | = | \( 8978 = 2 \cdot 67^{2} \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Sturm bound: | \(10073316\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8978))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2524929 | 839070 | 1685859 |
| Cusp forms | 2511730 | 839070 | 1672660 |
| Eisenstein series | 13199 | 0 | 13199 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8978))\)
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 |
|---|---|---|---|---|
| 8978.2.a | \(\chi_{8978}(1, \cdot)\) | 8978.2.a.a | 1 | 1 |
| 8978.2.a.b | 1 | |||
| 8978.2.a.c | 2 | |||
| 8978.2.a.d | 2 | |||
| 8978.2.a.e | 2 | |||
| 8978.2.a.f | 2 | |||
| 8978.2.a.g | 3 | |||
| 8978.2.a.h | 3 | |||
| 8978.2.a.i | 3 | |||
| 8978.2.a.j | 3 | |||
| 8978.2.a.k | 15 | |||
| 8978.2.a.l | 15 | |||
| 8978.2.a.m | 16 | |||
| 8978.2.a.n | 16 | |||
| 8978.2.a.o | 20 | |||
| 8978.2.a.p | 20 | |||
| 8978.2.a.q | 20 | |||
| 8978.2.a.r | 20 | |||
| 8978.2.a.s | 24 | |||
| 8978.2.a.t | 24 | |||
| 8978.2.a.u | 30 | |||
| 8978.2.a.v | 30 | |||
| 8978.2.a.w | 48 | |||
| 8978.2.a.x | 48 | |||
| 8978.2.c | \(\chi_{8978}(699, \cdot)\) | n/a | 738 | 2 |
| 8978.2.e | \(\chi_{8978}(143, \cdot)\) | n/a | 3670 | 10 |
| 8978.2.g | \(\chi_{8978}(875, \cdot)\) | n/a | 7380 | 20 |
| 8978.2.i | \(\chi_{8978}(135, \cdot)\) | n/a | 25146 | 66 |
| 8978.2.k | \(\chi_{8978}(29, \cdot)\) | n/a | 50028 | 132 |
| 8978.2.m | \(\chi_{8978}(9, \cdot)\) | n/a | 251460 | 660 |
| 8978.2.o | \(\chi_{8978}(17, \cdot)\) | n/a | 500280 | 1320 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8978))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(8978)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4489))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8978))\)\(^{\oplus 1}\)