Defining parameters
Level: | \( N \) | \(=\) | \( 333 = 3^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 333.u (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 333 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(114\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(333, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 156 | 156 | 0 |
Cusp forms | 148 | 148 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(333, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
333.3.u.a | $148$ | $9.074$ | None | \(-3\) | \(-2\) | \(-21\) | \(-4\) |