Defining parameters
| Level: | \( N \) | = | \( 6889 = 83^{2} \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Sturm bound: | \(7908572\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6889))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1982227 | 1981571 | 656 |
| Cusp forms | 1972060 | 1971566 | 494 |
| Eisenstein series | 10167 | 10005 | 162 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6889))\)
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 |
|---|---|---|---|---|
| 6889.2.a | \(\chi_{6889}(1, \cdot)\) | 6889.2.a.a | 1 | 1 |
| 6889.2.a.b | 2 | |||
| 6889.2.a.c | 3 | |||
| 6889.2.a.d | 4 | |||
| 6889.2.a.e | 6 | |||
| 6889.2.a.f | 7 | |||
| 6889.2.a.g | 7 | |||
| 6889.2.a.h | 10 | |||
| 6889.2.a.i | 24 | |||
| 6889.2.a.j | 24 | |||
| 6889.2.a.k | 42 | |||
| 6889.2.a.l | 42 | |||
| 6889.2.a.m | 42 | |||
| 6889.2.a.n | 72 | |||
| 6889.2.a.o | 120 | |||
| 6889.2.a.p | 120 | |||
| 6889.2.c | \(\chi_{6889}(99, \cdot)\) | n/a | 21080 | 40 |
| 6889.2.e | \(\chi_{6889}(84, \cdot)\) | n/a | 47560 | 82 |
| 6889.2.g | \(\chi_{6889}(3, \cdot)\) | n/a | 1902400 | 3280 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6889))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(6889)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(83))\)\(^{\oplus 2}\)