Defining parameters
| Level: | \( N \) | = | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(1344\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(156))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 131 | 28 | 103 |
| Cusp forms | 11 | 4 | 7 |
| Eisenstein series | 120 | 24 | 96 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(156))\)
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 |
|---|---|---|---|---|
| 156.1.d | \(\chi_{156}(53, \cdot)\) | None | 0 | 1 |
| 156.1.e | \(\chi_{156}(103, \cdot)\) | None | 0 | 1 |
| 156.1.f | \(\chi_{156}(79, \cdot)\) | None | 0 | 1 |
| 156.1.g | \(\chi_{156}(77, \cdot)\) | None | 0 | 1 |
| 156.1.j | \(\chi_{156}(73, \cdot)\) | None | 0 | 2 |
| 156.1.l | \(\chi_{156}(47, \cdot)\) | None | 0 | 2 |
| 156.1.n | \(\chi_{156}(43, \cdot)\) | None | 0 | 2 |
| 156.1.o | \(\chi_{156}(29, \cdot)\) | 156.1.o.a | 2 | 2 |
| 156.1.s | \(\chi_{156}(17, \cdot)\) | 156.1.s.a | 2 | 2 |
| 156.1.t | \(\chi_{156}(55, \cdot)\) | None | 0 | 2 |
| 156.1.v | \(\chi_{156}(11, \cdot)\) | None | 0 | 4 |
| 156.1.x | \(\chi_{156}(37, \cdot)\) | None | 0 | 4 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(156))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(156)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)