Defining parameters
| Level: | \( N \) | = | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 6 \) | ||
| Newform subspaces: | \( 8 \) | ||
| Sturm bound: | \(4032\) | ||
| Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(260))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 262 | 86 | 176 |
| Cusp forms | 22 | 18 | 4 |
| Eisenstein series | 240 | 68 | 172 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 18 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(260))\)
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 the newforms together with their dimension.
| Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
|---|---|---|---|---|
| 260.1.b | \(\chi_{260}(131, \cdot)\) | None | 0 | 1 |
| 260.1.e | \(\chi_{260}(51, \cdot)\) | None | 0 | 1 |
| 260.1.g | \(\chi_{260}(259, \cdot)\) | 260.1.g.a | 1 | 1 |
| 260.1.g.b | 1 | |||
| 260.1.h | \(\chi_{260}(79, \cdot)\) | None | 0 | 1 |
| 260.1.k | \(\chi_{260}(109, \cdot)\) | None | 0 | 2 |
| 260.1.l | \(\chi_{260}(47, \cdot)\) | 260.1.l.a | 2 | 2 |
| 260.1.n | \(\chi_{260}(77, \cdot)\) | None | 0 | 2 |
| 260.1.q | \(\chi_{260}(53, \cdot)\) | None | 0 | 2 |
| 260.1.s | \(\chi_{260}(187, \cdot)\) | 260.1.s.a | 2 | 2 |
| 260.1.t | \(\chi_{260}(21, \cdot)\) | None | 0 | 2 |
| 260.1.v | \(\chi_{260}(139, \cdot)\) | None | 0 | 2 |
| 260.1.w | \(\chi_{260}(179, \cdot)\) | 260.1.w.a | 2 | 2 |
| 260.1.w.b | 2 | |||
| 260.1.y | \(\chi_{260}(231, \cdot)\) | None | 0 | 2 |
| 260.1.bb | \(\chi_{260}(191, \cdot)\) | None | 0 | 2 |
| 260.1.bd | \(\chi_{260}(41, \cdot)\) | None | 0 | 4 |
| 260.1.be | \(\chi_{260}(63, \cdot)\) | 260.1.be.a | 4 | 4 |
| 260.1.bh | \(\chi_{260}(113, \cdot)\) | None | 0 | 4 |
| 260.1.bi | \(\chi_{260}(17, \cdot)\) | None | 0 | 4 |
| 260.1.bl | \(\chi_{260}(7, \cdot)\) | 260.1.bl.a | 4 | 4 |
| 260.1.bm | \(\chi_{260}(89, \cdot)\) | None | 0 | 4 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(260))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(260)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)