Defining parameters
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.s (of order \(14\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 392 \) |
Character field: | \(\Q(\zeta_{14})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(392, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 684 | 684 | 0 |
Cusp forms | 660 | 660 | 0 |
Eisenstein series | 24 | 24 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(392, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
392.3.s.a | $660$ | $10.681$ | None | \(-5\) | \(-10\) | \(0\) | \(0\) |