Defining parameters
| Level: | \( N \) | = | \( 539 = 7^{2} \cdot 11 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 5 \) | ||
| Newform subspaces: | \( 7 \) | ||
| Sturm bound: | \(23520\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(539))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 637 | 466 | 171 |
| Cusp forms | 37 | 29 | 8 |
| Eisenstein series | 600 | 437 | 163 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 29 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(539))\)
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 |
|---|---|---|---|---|
| 539.1.c | \(\chi_{539}(197, \cdot)\) | 539.1.c.a | 1 | 1 |
| 539.1.c.b | 2 | |||
| 539.1.d | \(\chi_{539}(342, \cdot)\) | None | 0 | 1 |
| 539.1.g | \(\chi_{539}(166, \cdot)\) | None | 0 | 2 |
| 539.1.h | \(\chi_{539}(263, \cdot)\) | 539.1.h.a | 2 | 2 |
| 539.1.h.b | 4 | |||
| 539.1.k | \(\chi_{539}(48, \cdot)\) | None | 0 | 4 |
| 539.1.l | \(\chi_{539}(50, \cdot)\) | 539.1.l.a | 4 | 4 |
| 539.1.n | \(\chi_{539}(34, \cdot)\) | None | 0 | 6 |
| 539.1.o | \(\chi_{539}(43, \cdot)\) | None | 0 | 6 |
| 539.1.t | \(\chi_{539}(18, \cdot)\) | 539.1.t.a | 8 | 8 |
| 539.1.u | \(\chi_{539}(31, \cdot)\) | 539.1.u.a | 8 | 8 |
| 539.1.x | \(\chi_{539}(32, \cdot)\) | None | 0 | 12 |
| 539.1.y | \(\chi_{539}(12, \cdot)\) | None | 0 | 12 |
| 539.1.ba | \(\chi_{539}(8, \cdot)\) | None | 0 | 24 |
| 539.1.bb | \(\chi_{539}(20, \cdot)\) | None | 0 | 24 |
| 539.1.bd | \(\chi_{539}(3, \cdot)\) | None | 0 | 48 |
| 539.1.be | \(\chi_{539}(2, \cdot)\) | None | 0 | 48 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(539))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(539)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 1}\)