Defining parameters
| Level: | \( N \) | = | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(3072\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(240))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 234 | 30 | 204 |
| Cusp forms | 10 | 4 | 6 |
| Eisenstein series | 224 | 26 | 198 |
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 \(S_{1}^{\mathrm{new}}(\Gamma_1(240))\)
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 |
|---|---|---|---|---|
| 240.1.c | \(\chi_{240}(209, \cdot)\) | None | 0 | 1 |
| 240.1.e | \(\chi_{240}(31, \cdot)\) | None | 0 | 1 |
| 240.1.g | \(\chi_{240}(151, \cdot)\) | None | 0 | 1 |
| 240.1.i | \(\chi_{240}(89, \cdot)\) | None | 0 | 1 |
| 240.1.j | \(\chi_{240}(79, \cdot)\) | None | 0 | 1 |
| 240.1.l | \(\chi_{240}(161, \cdot)\) | None | 0 | 1 |
| 240.1.n | \(\chi_{240}(41, \cdot)\) | None | 0 | 1 |
| 240.1.p | \(\chi_{240}(199, \cdot)\) | None | 0 | 1 |
| 240.1.q | \(\chi_{240}(19, \cdot)\) | None | 0 | 2 |
| 240.1.r | \(\chi_{240}(101, \cdot)\) | None | 0 | 2 |
| 240.1.u | \(\chi_{240}(23, \cdot)\) | None | 0 | 2 |
| 240.1.x | \(\chi_{240}(73, \cdot)\) | None | 0 | 2 |
| 240.1.z | \(\chi_{240}(83, \cdot)\) | None | 0 | 2 |
| 240.1.ba | \(\chi_{240}(13, \cdot)\) | None | 0 | 2 |
| 240.1.bd | \(\chi_{240}(203, \cdot)\) | None | 0 | 2 |
| 240.1.be | \(\chi_{240}(133, \cdot)\) | None | 0 | 2 |
| 240.1.bg | \(\chi_{240}(97, \cdot)\) | None | 0 | 2 |
| 240.1.bj | \(\chi_{240}(47, \cdot)\) | None | 0 | 2 |
| 240.1.bm | \(\chi_{240}(29, \cdot)\) | 240.1.bm.a | 4 | 2 |
| 240.1.bn | \(\chi_{240}(91, \cdot)\) | None | 0 | 2 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(240))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(240)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(240))\)\(^{\oplus 1}\)