Defining parameters
| Level: | \( N \) | \(=\) | \( 3584 = 2^{9} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 3584.bf (of order \(16\) and degree \(8\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 448 \) |
| Character field: | \(\Q(\zeta_{16})\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(512\) | ||
| Trace bound: | \(63\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3584, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 192 | 48 | 144 |
| Cusp forms | 64 | 16 | 48 |
| Eisenstein series | 128 | 32 | 96 |
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 \(S_{1}^{\mathrm{new}}(3584, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 3584.1.bf.a | $8$ | $1.789$ | \(\Q(\zeta_{16})\) | $D_{16}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{16}q^{7}-\zeta_{16}^{7}q^{9}+(\zeta_{16}^{3}+\zeta_{16}^{6}+\cdots)q^{11}+\cdots\) |
| 3584.1.bf.b | $8$ | $1.789$ | \(\Q(\zeta_{16})\) | $D_{16}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{16}q^{7}-\zeta_{16}^{7}q^{9}+(-\zeta_{16}^{3}-\zeta_{16}^{6}+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3584, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3584, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1792, [\chi])\)\(^{\oplus 2}\)