Defining parameters
Level: | \( N \) | \(=\) | \( 387 = 3^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 387.o (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 387 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(132\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(387, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 180 | 180 | 0 |
Cusp forms | 172 | 172 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(387, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
387.3.o.a | $172$ | $10.545$ | None | \(-6\) | \(-5\) | \(0\) | \(2\) |