Defining parameters
| Level: | \( N \) | = | \( 279 = 3^{2} \cdot 31 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(5760\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(279))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 259 | 139 | 120 |
| Cusp forms | 19 | 8 | 11 |
| Eisenstein series | 240 | 131 | 109 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 8 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(279))\)
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 |
|---|---|---|---|---|
| 279.1.b | \(\chi_{279}(125, \cdot)\) | None | 0 | 1 |
| 279.1.d | \(\chi_{279}(154, \cdot)\) | 279.1.d.a | 1 | 1 |
| 279.1.d.b | 1 | |||
| 279.1.d.c | 2 | |||
| 279.1.k | \(\chi_{279}(98, \cdot)\) | None | 0 | 2 |
| 279.1.l | \(\chi_{279}(88, \cdot)\) | None | 0 | 2 |
| 279.1.m | \(\chi_{279}(61, \cdot)\) | None | 0 | 2 |
| 279.1.n | \(\chi_{279}(223, \cdot)\) | None | 0 | 2 |
| 279.1.p | \(\chi_{279}(5, \cdot)\) | None | 0 | 2 |
| 279.1.q | \(\chi_{279}(149, \cdot)\) | None | 0 | 2 |
| 279.1.t | \(\chi_{279}(32, \cdot)\) | None | 0 | 2 |
| 279.1.u | \(\chi_{279}(37, \cdot)\) | None | 0 | 2 |
| 279.1.v | \(\chi_{279}(46, \cdot)\) | 279.1.v.a | 4 | 4 |
| 279.1.x | \(\chi_{279}(8, \cdot)\) | None | 0 | 4 |
| 279.1.bc | \(\chi_{279}(55, \cdot)\) | None | 0 | 8 |
| 279.1.bd | \(\chi_{279}(38, \cdot)\) | None | 0 | 8 |
| 279.1.bf | \(\chi_{279}(2, \cdot)\) | None | 0 | 8 |
| 279.1.bi | \(\chi_{279}(14, \cdot)\) | None | 0 | 8 |
| 279.1.bj | \(\chi_{279}(58, \cdot)\) | None | 0 | 8 |
| 279.1.bk | \(\chi_{279}(52, \cdot)\) | None | 0 | 8 |
| 279.1.bl | \(\chi_{279}(13, \cdot)\) | None | 0 | 8 |
| 279.1.bm | \(\chi_{279}(71, \cdot)\) | None | 0 | 8 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(279))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(279)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 2}\)