Defining parameters
| Level: | \( N \) | = | \( 345 = 3 \cdot 5 \cdot 23 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(8448\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(345))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 376 | 148 | 228 |
| Cusp forms | 24 | 20 | 4 |
| Eisenstein series | 352 | 128 | 224 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 20 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(345))\)
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 |
|---|---|---|---|---|
| 345.1.d | \(\chi_{345}(229, \cdot)\) | None | 0 | 1 |
| 345.1.e | \(\chi_{345}(116, \cdot)\) | None | 0 | 1 |
| 345.1.f | \(\chi_{345}(254, \cdot)\) | None | 0 | 1 |
| 345.1.g | \(\chi_{345}(91, \cdot)\) | None | 0 | 1 |
| 345.1.k | \(\chi_{345}(208, \cdot)\) | None | 0 | 2 |
| 345.1.l | \(\chi_{345}(68, \cdot)\) | None | 0 | 2 |
| 345.1.o | \(\chi_{345}(61, \cdot)\) | None | 0 | 10 |
| 345.1.p | \(\chi_{345}(29, \cdot)\) | 345.1.p.a | 10 | 10 |
| 345.1.p.b | 10 | |||
| 345.1.q | \(\chi_{345}(26, \cdot)\) | None | 0 | 10 |
| 345.1.r | \(\chi_{345}(19, \cdot)\) | None | 0 | 10 |
| 345.1.u | \(\chi_{345}(17, \cdot)\) | None | 0 | 20 |
| 345.1.v | \(\chi_{345}(13, \cdot)\) | None | 0 | 20 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(345))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(345)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 1}\)