Defining parameters
| Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1008.u (of order \(4\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 112 \) |
| Character field: | \(\Q(i)\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(192\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1008, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 28 | 10 | 18 |
| Cusp forms | 12 | 6 | 6 |
| Eisenstein series | 16 | 4 | 12 |
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 \(S_{1}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 1008.1.u.a | $2$ | $0.503$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-7}) \) | None | \(-2\) | \(0\) | \(0\) | \(0\) | \(q-q^{2}+q^{4}+i q^{7}-q^{8}+(-i+1)q^{11}+\cdots\) |
| 1008.1.u.b | $2$ | $0.503$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+i q^{2}-q^{4}-i q^{7}-i q^{8}+(-i+1)q^{11}+\cdots\) |
| 1008.1.u.c | $2$ | $0.503$ | \(\Q(\sqrt{-1}) \) | $D_{4}$ | \(\Q(\sqrt{-7}) \) | None | \(2\) | \(0\) | \(0\) | \(0\) | \(q+q^{2}+q^{4}+i q^{7}+q^{8}+(i-1)q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1008, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)