Defining parameters
| Level: | \( N \) | = | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(3456\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(252))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 253 | 50 | 203 |
| Cusp forms | 13 | 6 | 7 |
| Eisenstein series | 240 | 44 | 196 |
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 \(S_{1}^{\mathrm{new}}(\Gamma_1(252))\)
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 |
|---|---|---|---|---|
| 252.1.c | \(\chi_{252}(197, \cdot)\) | None | 0 | 1 |
| 252.1.d | \(\chi_{252}(181, \cdot)\) | None | 0 | 1 |
| 252.1.g | \(\chi_{252}(127, \cdot)\) | None | 0 | 1 |
| 252.1.h | \(\chi_{252}(251, \cdot)\) | 252.1.h.a | 4 | 1 |
| 252.1.m | \(\chi_{252}(65, \cdot)\) | None | 0 | 2 |
| 252.1.p | \(\chi_{252}(61, \cdot)\) | None | 0 | 2 |
| 252.1.q | \(\chi_{252}(143, \cdot)\) | None | 0 | 2 |
| 252.1.r | \(\chi_{252}(131, \cdot)\) | None | 0 | 2 |
| 252.1.s | \(\chi_{252}(83, \cdot)\) | None | 0 | 2 |
| 252.1.u | \(\chi_{252}(151, \cdot)\) | None | 0 | 2 |
| 252.1.v | \(\chi_{252}(43, \cdot)\) | None | 0 | 2 |
| 252.1.y | \(\chi_{252}(163, \cdot)\) | None | 0 | 2 |
| 252.1.z | \(\chi_{252}(73, \cdot)\) | 252.1.z.a | 2 | 2 |
| 252.1.bc | \(\chi_{252}(13, \cdot)\) | None | 0 | 2 |
| 252.1.bd | \(\chi_{252}(229, \cdot)\) | None | 0 | 2 |
| 252.1.bg | \(\chi_{252}(29, \cdot)\) | None | 0 | 2 |
| 252.1.bh | \(\chi_{252}(137, \cdot)\) | None | 0 | 2 |
| 252.1.bk | \(\chi_{252}(53, \cdot)\) | None | 0 | 2 |
| 252.1.bl | \(\chi_{252}(67, \cdot)\) | None | 0 | 2 |
| 252.1.bn | \(\chi_{252}(47, \cdot)\) | None | 0 | 2 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(252))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(252)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)