Defining parameters
| Level: | \( N \) | = | \( 152 = 2^{3} \cdot 19 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(1440\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(152))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 120 | 44 | 76 |
| Cusp forms | 12 | 10 | 2 |
| Eisenstein series | 108 | 34 | 74 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 10 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(152))\)
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 |
|---|---|---|---|---|
| 152.1.d | \(\chi_{152}(39, \cdot)\) | None | 0 | 1 |
| 152.1.e | \(\chi_{152}(113, \cdot)\) | None | 0 | 1 |
| 152.1.f | \(\chi_{152}(115, \cdot)\) | None | 0 | 1 |
| 152.1.g | \(\chi_{152}(37, \cdot)\) | 152.1.g.a | 1 | 1 |
| 152.1.g.b | 1 | |||
| 152.1.k | \(\chi_{152}(11, \cdot)\) | 152.1.k.a | 2 | 2 |
| 152.1.l | \(\chi_{152}(69, \cdot)\) | None | 0 | 2 |
| 152.1.m | \(\chi_{152}(7, \cdot)\) | None | 0 | 2 |
| 152.1.n | \(\chi_{152}(65, \cdot)\) | None | 0 | 2 |
| 152.1.r | \(\chi_{152}(33, \cdot)\) | None | 0 | 6 |
| 152.1.s | \(\chi_{152}(13, \cdot)\) | None | 0 | 6 |
| 152.1.u | \(\chi_{152}(35, \cdot)\) | 152.1.u.a | 6 | 6 |
| 152.1.x | \(\chi_{152}(23, \cdot)\) | None | 0 | 6 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(152))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(152)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)