Defining parameters
| Level: | \( N \) | \(=\) | \( 13 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 13.e (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(4\) | ||
| Trace bound: | \(2\) | ||
| Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(13, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 8 | 8 | 0 |
| Cusp forms | 4 | 4 | 0 |
| Eisenstein series | 4 | 4 | 0 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(13, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 13.4.e.a | $2$ | $0.767$ | \(\Q(\sqrt{-3}) \) | None | \(-6\) | \(7\) | \(0\) | \(39\) | \(q+(-2-2\zeta_{6})q^{2}+(7-7\zeta_{6})q^{3}+4\zeta_{6}q^{4}+\cdots\) |
| 13.4.e.b | $2$ | $0.767$ | \(\Q(\sqrt{-3}) \) | None | \(3\) | \(-2\) | \(0\) | \(-24\) | \(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}-5\zeta_{6}q^{4}+\cdots\) |