Defining parameters
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.p (of order \(30\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 99 \) |
Character field: | \(\Q(\zeta_{30})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(99, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 496 | 496 | 0 |
Cusp forms | 464 | 464 | 0 |
Eisenstein series | 32 | 32 | 0 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(99, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
99.6.p.a | $464$ | $15.878$ | None | \(-15\) | \(-27\) | \(-96\) | \(-5\) |