Defining parameters
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.e (of order \(16\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 17 \) |
Character field: | \(\Q(\zeta_{16})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(4\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(17, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 32 | 32 | 0 |
Cusp forms | 16 | 16 | 0 |
Eisenstein series | 16 | 16 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(17, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
17.3.e.a | $8$ | $0.463$ | \(\Q(\zeta_{16})\) | None | \(-8\) | \(-8\) | \(16\) | \(8\) | \(q+(-1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{2}+\cdots\) |
17.3.e.b | $8$ | $0.463$ | \(\Q(\zeta_{16})\) | None | \(0\) | \(0\) | \(-24\) | \(-16\) | \(q+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\zeta_{16}^{7})q^{2}+(2\zeta_{16}^{2}+\cdots)q^{3}+\cdots\) |