Defining parameters
| Level: | \( N \) | = | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(16896\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(552))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 560 | 90 | 470 |
| Cusp forms | 32 | 6 | 26 |
| Eisenstein series | 528 | 84 | 444 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(552))\)
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 |
|---|---|---|---|---|
| 552.1.c | \(\chi_{552}(505, \cdot)\) | None | 0 | 1 |
| 552.1.d | \(\chi_{552}(139, \cdot)\) | None | 0 | 1 |
| 552.1.g | \(\chi_{552}(185, \cdot)\) | None | 0 | 1 |
| 552.1.h | \(\chi_{552}(275, \cdot)\) | 552.1.h.a | 1 | 1 |
| 552.1.h.b | 1 | |||
| 552.1.h.c | 2 | |||
| 552.1.h.d | 2 | |||
| 552.1.k | \(\chi_{552}(415, \cdot)\) | None | 0 | 1 |
| 552.1.l | \(\chi_{552}(229, \cdot)\) | None | 0 | 1 |
| 552.1.o | \(\chi_{552}(551, \cdot)\) | None | 0 | 1 |
| 552.1.p | \(\chi_{552}(461, \cdot)\) | None | 0 | 1 |
| 552.1.r | \(\chi_{552}(29, \cdot)\) | None | 0 | 10 |
| 552.1.s | \(\chi_{552}(143, \cdot)\) | None | 0 | 10 |
| 552.1.v | \(\chi_{552}(37, \cdot)\) | None | 0 | 10 |
| 552.1.w | \(\chi_{552}(31, \cdot)\) | None | 0 | 10 |
| 552.1.z | \(\chi_{552}(11, \cdot)\) | None | 0 | 10 |
| 552.1.ba | \(\chi_{552}(41, \cdot)\) | None | 0 | 10 |
| 552.1.bd | \(\chi_{552}(163, \cdot)\) | None | 0 | 10 |
| 552.1.be | \(\chi_{552}(97, \cdot)\) | None | 0 | 10 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(552))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(552)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 2}\)