Defining parameters
| Level: | \( N \) | = | \( 98 = 2 \cdot 7^{2} \) |
| Weight: | \( k \) | = | \( 6 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Newform subspaces: | \( 22 \) | ||
| Sturm bound: | \(3528\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(98))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1530 | 470 | 1060 |
| Cusp forms | 1410 | 470 | 940 |
| Eisenstein series | 120 | 0 | 120 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(98))\)
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 |
|---|---|---|---|---|
| 98.6.a | \(\chi_{98}(1, \cdot)\) | 98.6.a.a | 1 | 1 |
| 98.6.a.b | 1 | |||
| 98.6.a.c | 2 | |||
| 98.6.a.d | 2 | |||
| 98.6.a.e | 2 | |||
| 98.6.a.f | 2 | |||
| 98.6.a.g | 2 | |||
| 98.6.a.h | 2 | |||
| 98.6.a.i | 4 | |||
| 98.6.c | \(\chi_{98}(67, \cdot)\) | 98.6.c.a | 2 | 2 |
| 98.6.c.b | 2 | |||
| 98.6.c.c | 2 | |||
| 98.6.c.d | 2 | |||
| 98.6.c.e | 4 | |||
| 98.6.c.f | 4 | |||
| 98.6.c.g | 4 | |||
| 98.6.c.h | 4 | |||
| 98.6.c.i | 8 | |||
| 98.6.e | \(\chi_{98}(15, \cdot)\) | 98.6.e.a | 66 | 6 |
| 98.6.e.b | 66 | |||
| 98.6.g | \(\chi_{98}(9, \cdot)\) | 98.6.g.a | 144 | 12 |
| 98.6.g.b | 144 |
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(98))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(98)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)