Defining parameters
| Level: | \( N \) | = | \( 1083 = 3 \cdot 19^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 5 \) | ||
| Newform subspaces: | \( 7 \) | ||
| Sturm bound: | \(86640\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1083))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1082 | 539 | 543 |
| Cusp forms | 74 | 70 | 4 |
| Eisenstein series | 1008 | 469 | 539 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 70 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1083))\)
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 |
|---|---|---|---|---|
| 1083.1.b | \(\chi_{1083}(362, \cdot)\) | 1083.1.b.a | 1 | 1 |
| 1083.1.b.b | 1 | |||
| 1083.1.c | \(\chi_{1083}(721, \cdot)\) | None | 0 | 1 |
| 1083.1.g | \(\chi_{1083}(430, \cdot)\) | None | 0 | 2 |
| 1083.1.h | \(\chi_{1083}(68, \cdot)\) | 1083.1.h.a | 2 | 2 |
| 1083.1.k | \(\chi_{1083}(127, \cdot)\) | None | 0 | 6 |
| 1083.1.l | \(\chi_{1083}(62, \cdot)\) | 1083.1.l.a | 6 | 6 |
| 1083.1.l.b | 6 | |||
| 1083.1.o | \(\chi_{1083}(37, \cdot)\) | None | 0 | 18 |
| 1083.1.p | \(\chi_{1083}(20, \cdot)\) | 1083.1.p.a | 18 | 18 |
| 1083.1.r | \(\chi_{1083}(11, \cdot)\) | 1083.1.r.a | 36 | 36 |
| 1083.1.s | \(\chi_{1083}(31, \cdot)\) | None | 0 | 36 |
| 1083.1.v | \(\chi_{1083}(5, \cdot)\) | None | 0 | 108 |
| 1083.1.w | \(\chi_{1083}(10, \cdot)\) | None | 0 | 108 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1083))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1083)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 1}\)