Defining parameters
| Level: | \( N \) | \(=\) | \( 2944 = 2^{7} \cdot 23 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2944.e (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 184 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(384\) | ||
| Trace bound: | \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2944, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 44 | 4 | 40 |
| Cusp forms | 28 | 4 | 24 |
| Eisenstein series | 16 | 0 | 16 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 4 | 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.e.a | $2$ | $1.469$ | \(\Q(\sqrt{2}) \) | $D_{4}$ | \(\Q(\sqrt{-46}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta q^{5}+q^{9}-\beta q^{11}+\beta q^{19}-q^{23}+\cdots\) |
| 2944.1.e.b | $2$ | $1.469$ | \(\Q(\sqrt{2}) \) | $D_{4}$ | \(\Q(\sqrt{-46}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta q^{5}+q^{9}-\beta q^{11}+\beta q^{19}+q^{23}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2944, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2944, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(184, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(736, [\chi])\)\(^{\oplus 3}\)