Defining parameters
| Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2352.by (of order \(14\) and degree \(6\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 588 \) |
| Character field: | \(\Q(\zeta_{14})\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(448\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2352, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 84 | 12 | 72 |
| Cusp forms | 12 | 12 | 0 |
| Eisenstein series | 72 | 0 | 72 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 12 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||||
| 2352.1.by.a | \(6\) | \(1.174\) | \(\Q(\zeta_{14})\) | \(D_{14}\) | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-1\) | \(0\) | \(1\) | \(q-\zeta_{14}q^{3}+\zeta_{14}^{5}q^{7}+\zeta_{14}^{2}q^{9}+(-\zeta_{14}^{4}+\cdots)q^{13}+\cdots\) |
| 2352.1.by.b | \(6\) | \(1.174\) | \(\Q(\zeta_{14})\) | \(D_{14}\) | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(1\) | \(0\) | \(-1\) | \(q+\zeta_{14}q^{3}-\zeta_{14}^{5}q^{7}+\zeta_{14}^{2}q^{9}+(-\zeta_{14}^{4}+\cdots)q^{13}+\cdots\) |