Defining parameters
| Level: | \( N \) | = | \( 667 = 23 \cdot 29 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 6 \) | ||
| Sturm bound: | \(36960\) | ||
| Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(667))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 657 | 605 | 52 |
| Cusp forms | 41 | 39 | 2 |
| Eisenstein series | 616 | 566 | 50 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 39 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(667))\)
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 |
|---|---|---|---|---|
| 667.1.b | \(\chi_{667}(666, \cdot)\) | 667.1.b.a | 1 | 1 |
| 667.1.b.b | 2 | |||
| 667.1.d | \(\chi_{667}(436, \cdot)\) | None | 0 | 1 |
| 667.1.e | \(\chi_{667}(70, \cdot)\) | None | 0 | 2 |
| 667.1.i | \(\chi_{667}(45, \cdot)\) | 667.1.i.a | 6 | 6 |
| 667.1.i.b | 12 | |||
| 667.1.k | \(\chi_{667}(22, \cdot)\) | 667.1.k.a | 6 | 6 |
| 667.1.k.b | 12 | |||
| 667.1.l | \(\chi_{667}(30, \cdot)\) | None | 0 | 10 |
| 667.1.n | \(\chi_{667}(28, \cdot)\) | None | 0 | 10 |
| 667.1.p | \(\chi_{667}(47, \cdot)\) | None | 0 | 12 |
| 667.1.r | \(\chi_{667}(12, \cdot)\) | None | 0 | 20 |
| 667.1.t | \(\chi_{667}(5, \cdot)\) | None | 0 | 60 |
| 667.1.v | \(\chi_{667}(7, \cdot)\) | None | 0 | 60 |
| 667.1.w | \(\chi_{667}(2, \cdot)\) | None | 0 | 120 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(667))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(667)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)