Defining parameters
| Level: | \( N \) | \(=\) | \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3528.co (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 504 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(672\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3528, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 48 | 32 | 16 |
| Cusp forms | 16 | 16 | 0 |
| Eisenstein series | 32 | 16 | 16 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 16 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3528, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||||
| 3528.1.co.a | \(16\) | \(1.761\) | \(\Q(\zeta_{48})\) | \(D_{24}\) | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{48}^{20}q^{2}+\zeta_{48}^{5}q^{3}-\zeta_{48}^{16}q^{4}+\cdots\) |