Defining parameters
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.d (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(45\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(38, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 84 | 24 | 60 |
Cusp forms | 76 | 24 | 52 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(38, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
38.9.d.a | $24$ | $15.480$ | None | \(0\) | \(168\) | \(-558\) | \(11992\) |
Decomposition of \(S_{9}^{\mathrm{old}}(38, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)