Defining parameters
| Level: | \( N \) | = | \( 2401 = 7^{4} \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Sturm bound: | \(941192\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2401))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 237650 | 227628 | 10022 |
| Cusp forms | 232947 | 223956 | 8991 |
| Eisenstein series | 4703 | 3672 | 1031 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2401))\)
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 |
|---|---|---|---|---|
| 2401.2.a | \(\chi_{2401}(1, \cdot)\) | 2401.2.a.a | 3 | 1 |
| 2401.2.a.b | 3 | |||
| 2401.2.a.c | 6 | |||
| 2401.2.a.d | 6 | |||
| 2401.2.a.e | 9 | |||
| 2401.2.a.f | 9 | |||
| 2401.2.a.g | 18 | |||
| 2401.2.a.h | 24 | |||
| 2401.2.a.i | 24 | |||
| 2401.2.a.j | 48 | |||
| 2401.2.c | \(\chi_{2401}(1047, \cdot)\) | n/a | 300 | 2 |
| 2401.2.e | \(\chi_{2401}(344, \cdot)\) | n/a | 918 | 6 |
| 2401.2.g | \(\chi_{2401}(18, \cdot)\) | n/a | 1836 | 12 |
| 2401.2.i | \(\chi_{2401}(50, \cdot)\) | n/a | 6678 | 42 |
| 2401.2.k | \(\chi_{2401}(30, \cdot)\) | n/a | 13272 | 84 |
| 2401.2.m | \(\chi_{2401}(8, \cdot)\) | n/a | 66738 | 294 |
| 2401.2.o | \(\chi_{2401}(2, \cdot)\) | n/a | 134064 | 588 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2401))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(2401)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(343))\)\(^{\oplus 2}\)