Defining parameters
Level: | \( N \) | = | \( 289 = 17^{2} \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(27744\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(289))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 10604 | 10517 | 87 |
Cusp forms | 10204 | 10148 | 56 |
Eisenstein series | 400 | 369 | 31 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(289))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
289.4.a | \(\chi_{289}(1, \cdot)\) | 289.4.a.a | 1 | 1 |
289.4.a.b | 3 | |||
289.4.a.c | 4 | |||
289.4.a.d | 4 | |||
289.4.a.e | 4 | |||
289.4.a.f | 8 | |||
289.4.a.g | 12 | |||
289.4.a.h | 12 | |||
289.4.a.i | 12 | |||
289.4.b | \(\chi_{289}(288, \cdot)\) | 289.4.b.a | 2 | 1 |
289.4.b.b | 6 | |||
289.4.b.c | 8 | |||
289.4.b.d | 8 | |||
289.4.b.e | 12 | |||
289.4.b.f | 24 | |||
289.4.c | \(\chi_{289}(38, \cdot)\) | n/a | 120 | 2 |
289.4.d | \(\chi_{289}(110, \cdot)\) | n/a | 244 | 4 |
289.4.f | \(\chi_{289}(18, \cdot)\) | n/a | 1216 | 16 |
289.4.g | \(\chi_{289}(16, \cdot)\) | n/a | 1216 | 16 |
289.4.h | \(\chi_{289}(4, \cdot)\) | n/a | 2432 | 32 |
289.4.i | \(\chi_{289}(2, \cdot)\) | n/a | 4800 | 64 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(289))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(289)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)