Defining parameters
| Level: | \( N \) | = | \( 45 = 3^{2} \cdot 5 \) |
| Weight: | \( k \) | = | \( 16 \) |
| Nonzero newspaces: | \( 6 \) | ||
| Sturm bound: | \(2304\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(45))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1112 | 795 | 317 |
| Cusp forms | 1048 | 769 | 279 |
| Eisenstein series | 64 | 26 | 38 |
Trace form
Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(45))\)
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 |
|---|---|---|---|---|
| 45.16.a | \(\chi_{45}(1, \cdot)\) | 45.16.a.a | 2 | 1 |
| 45.16.a.b | 2 | |||
| 45.16.a.c | 2 | |||
| 45.16.a.d | 3 | |||
| 45.16.a.e | 3 | |||
| 45.16.a.f | 3 | |||
| 45.16.a.g | 5 | |||
| 45.16.a.h | 5 | |||
| 45.16.b | \(\chi_{45}(19, \cdot)\) | 45.16.b.a | 2 | 1 |
| 45.16.b.b | 6 | |||
| 45.16.b.c | 12 | |||
| 45.16.b.d | 16 | |||
| 45.16.e | \(\chi_{45}(16, \cdot)\) | n/a | 120 | 2 |
| 45.16.f | \(\chi_{45}(8, \cdot)\) | 45.16.f.a | 60 | 2 |
| 45.16.j | \(\chi_{45}(4, \cdot)\) | n/a | 176 | 2 |
| 45.16.l | \(\chi_{45}(2, \cdot)\) | n/a | 352 | 4 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces
\( S_{16}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)