Defining parameters
| Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 403.p (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 403 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(37\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(403, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 8 | 8 | 0 |
| Cusp forms | 4 | 4 | 0 |
| Eisenstein series | 4 | 4 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 0 | 4 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(403, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 403.1.p.a | $4$ | $0.201$ | \(\Q(\zeta_{12})\) | $A_{4}$ | None | None | \(-2\) | \(0\) | \(0\) | \(2\) | \(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}+\zeta_{12}q^{6}-\zeta_{12}^{4}q^{7}+\cdots\) |