Defining parameters
| Level: | \( N \) | = | \( 144 = 2^{4} \cdot 3^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(1152\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(144))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 117 | 21 | 96 |
| Cusp forms | 5 | 1 | 4 |
| Eisenstein series | 112 | 20 | 92 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 1 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(144))\)
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 |
|---|---|---|---|---|
| 144.1.b | \(\chi_{144}(55, \cdot)\) | None | 0 | 1 |
| 144.1.e | \(\chi_{144}(17, \cdot)\) | None | 0 | 1 |
| 144.1.g | \(\chi_{144}(127, \cdot)\) | 144.1.g.a | 1 | 1 |
| 144.1.h | \(\chi_{144}(89, \cdot)\) | None | 0 | 1 |
| 144.1.j | \(\chi_{144}(53, \cdot)\) | None | 0 | 2 |
| 144.1.m | \(\chi_{144}(19, \cdot)\) | None | 0 | 2 |
| 144.1.n | \(\chi_{144}(41, \cdot)\) | None | 0 | 2 |
| 144.1.o | \(\chi_{144}(31, \cdot)\) | None | 0 | 2 |
| 144.1.q | \(\chi_{144}(65, \cdot)\) | None | 0 | 2 |
| 144.1.t | \(\chi_{144}(7, \cdot)\) | None | 0 | 2 |
| 144.1.v | \(\chi_{144}(43, \cdot)\) | None | 0 | 4 |
| 144.1.w | \(\chi_{144}(5, \cdot)\) | None | 0 | 4 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(144)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)