Defining parameters
| Level: | \( N \) | \(=\) | \( 2944 = 2^{7} \cdot 23 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2944.p (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 736 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(384\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2944, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 80 | 20 | 60 |
| Cusp forms | 48 | 12 | 36 |
| Eisenstein series | 32 | 8 | 24 |
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 \(S_{1}^{\mathrm{new}}(2944, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 2944.1.p.a | $4$ | $1.469$ | \(\Q(\zeta_{8})\) | $D_{8}$ | \(\Q(\sqrt{-23}) \) | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q+(1+\zeta_{8}^{3})q^{3}+(1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{9}+\cdots\) |
| 2944.1.p.b | $8$ | $1.469$ | \(\Q(\zeta_{24})\) | $D_{24}$ | \(\Q(\sqrt{-23}) \) | None | \(0\) | \(-4\) | \(0\) | \(0\) | \(q+(-\zeta_{24}^{7}+\zeta_{24}^{8})q^{3}+(-\zeta_{24}^{2}+\zeta_{24}^{3}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2944, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2944, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(736, [\chi])\)\(^{\oplus 3}\)