Defining parameters
| Level: | \( N \) | = | \( 45 = 3^{2} \cdot 5 \) |
| Weight: | \( k \) | = | \( 18 \) |
| Nonzero newspaces: | \( 6 \) | ||
| Sturm bound: | \(2592\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(45))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1256 | 901 | 355 |
| Cusp forms | 1192 | 875 | 317 |
| Eisenstein series | 64 | 26 | 38 |
Trace form
Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(45))\)
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 |
|---|---|---|---|---|
| 45.18.a | \(\chi_{45}(1, \cdot)\) | 45.18.a.a | 2 | 1 |
| 45.18.a.b | 2 | |||
| 45.18.a.c | 3 | |||
| 45.18.a.d | 3 | |||
| 45.18.a.e | 3 | |||
| 45.18.a.f | 4 | |||
| 45.18.a.g | 6 | |||
| 45.18.a.h | 6 | |||
| 45.18.b | \(\chi_{45}(19, \cdot)\) | 45.18.b.a | 2 | 1 |
| 45.18.b.b | 8 | |||
| 45.18.b.c | 16 | |||
| 45.18.b.d | 16 | |||
| 45.18.e | \(\chi_{45}(16, \cdot)\) | n/a | 136 | 2 |
| 45.18.f | \(\chi_{45}(8, \cdot)\) | 45.18.f.a | 68 | 2 |
| 45.18.j | \(\chi_{45}(4, \cdot)\) | n/a | 200 | 2 |
| 45.18.l | \(\chi_{45}(2, \cdot)\) | n/a | 400 | 4 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces
\( S_{18}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 1}\)