Defining parameters
| Level: | \( N \) | = | \( 2523 = 3 \cdot 29^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Newform subspaces: | \( 10 \) | ||
| Sturm bound: | \(470960\) | ||
| Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2523))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2494 | 1231 | 1263 |
| Cusp forms | 86 | 82 | 4 |
| Eisenstein series | 2408 | 1149 | 1259 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 82 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2523))\)
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 |
|---|---|---|---|---|
| 2523.1.b | \(\chi_{2523}(842, \cdot)\) | 2523.1.b.a | 2 | 1 |
| 2523.1.b.b | 2 | |||
| 2523.1.b.c | 2 | |||
| 2523.1.d | \(\chi_{2523}(2522, \cdot)\) | 2523.1.d.a | 4 | 1 |
| 2523.1.e | \(\chi_{2523}(1723, \cdot)\) | None | 0 | 2 |
| 2523.1.h | \(\chi_{2523}(236, \cdot)\) | 2523.1.h.a | 6 | 6 |
| 2523.1.h.b | 6 | |||
| 2523.1.h.c | 24 | |||
| 2523.1.j | \(\chi_{2523}(605, \cdot)\) | 2523.1.j.a | 12 | 6 |
| 2523.1.j.b | 12 | |||
| 2523.1.j.c | 12 | |||
| 2523.1.l | \(\chi_{2523}(781, \cdot)\) | None | 0 | 12 |
| 2523.1.n | \(\chi_{2523}(86, \cdot)\) | None | 0 | 28 |
| 2523.1.p | \(\chi_{2523}(59, \cdot)\) | None | 0 | 28 |
| 2523.1.r | \(\chi_{2523}(46, \cdot)\) | None | 0 | 56 |
| 2523.1.t | \(\chi_{2523}(20, \cdot)\) | None | 0 | 168 |
| 2523.1.v | \(\chi_{2523}(5, \cdot)\) | None | 0 | 168 |
| 2523.1.w | \(\chi_{2523}(10, \cdot)\) | None | 0 | 336 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2523))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(2523)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(841))\)\(^{\oplus 2}\)