Defining parameters
| Level: | \( N \) | \(=\) | \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2016.dn (of order \(8\) and degree \(4\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 672 \) |
| Character field: | \(\Q(\zeta_{8})\) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(384\) | ||
| Trace bound: | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2016, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 48 | 16 | 32 |
| Cusp forms | 16 | 16 | 0 |
| Eisenstein series | 32 | 0 | 32 |
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 \(S_{1}^{\mathrm{new}}(2016, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 2016.1.dn.a | $4$ | $1.006$ | \(\Q(\zeta_{8})\) | $D_{8}$ | \(\Q(\sqrt{-7}) \) | None | \(-4\) | \(0\) | \(0\) | \(0\) | \(q-q^{2}+q^{4}+\zeta_{8}^{3}q^{7}-q^{8}+(-\zeta_{8}^{2}+\cdots)q^{11}+\cdots\) |
| 2016.1.dn.b | $4$ | $1.006$ | \(\Q(\zeta_{8})\) | $D_{8}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{8}+\cdots\) |
| 2016.1.dn.c | $4$ | $1.006$ | \(\Q(\zeta_{8})\) | $D_{8}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{8}+\cdots\) |
| 2016.1.dn.d | $4$ | $1.006$ | \(\Q(\zeta_{8})\) | $D_{8}$ | \(\Q(\sqrt{-7}) \) | None | \(4\) | \(0\) | \(0\) | \(0\) | \(q+q^{2}+q^{4}+\zeta_{8}^{3}q^{7}+q^{8}+(\zeta_{8}^{2}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots\) |