Defining parameters
| Level: | \( N \) | = | \( 648 = 2^{3} \cdot 3^{4} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Newform subspaces: | \( 6 \) | ||
| Sturm bound: | \(23328\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(648))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 724 | 142 | 582 |
| Cusp forms | 76 | 30 | 46 |
| Eisenstein series | 648 | 112 | 536 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 30 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(648))\)
We only show spaces with odd 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 |
|---|---|---|---|---|
| 648.1.b | \(\chi_{648}(163, \cdot)\) | 648.1.b.a | 1 | 1 |
| 648.1.b.b | 1 | |||
| 648.1.e | \(\chi_{648}(161, \cdot)\) | None | 0 | 1 |
| 648.1.g | \(\chi_{648}(487, \cdot)\) | None | 0 | 1 |
| 648.1.h | \(\chi_{648}(485, \cdot)\) | None | 0 | 1 |
| 648.1.j | \(\chi_{648}(53, \cdot)\) | 648.1.j.a | 2 | 2 |
| 648.1.j.b | 2 | |||
| 648.1.k | \(\chi_{648}(55, \cdot)\) | None | 0 | 2 |
| 648.1.m | \(\chi_{648}(377, \cdot)\) | None | 0 | 2 |
| 648.1.p | \(\chi_{648}(379, \cdot)\) | None | 0 | 2 |
| 648.1.r | \(\chi_{648}(19, \cdot)\) | 648.1.r.a | 6 | 6 |
| 648.1.s | \(\chi_{648}(127, \cdot)\) | None | 0 | 6 |
| 648.1.u | \(\chi_{648}(17, \cdot)\) | None | 0 | 6 |
| 648.1.x | \(\chi_{648}(125, \cdot)\) | None | 0 | 6 |
| 648.1.z | \(\chi_{648}(5, \cdot)\) | None | 0 | 18 |
| 648.1.ba | \(\chi_{648}(7, \cdot)\) | None | 0 | 18 |
| 648.1.bc | \(\chi_{648}(41, \cdot)\) | None | 0 | 18 |
| 648.1.bf | \(\chi_{648}(43, \cdot)\) | 648.1.bf.a | 18 | 18 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(648))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(648)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 2}\)