Defining parameters
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.f (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(15\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(38, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 72 | 24 | 48 |
Cusp forms | 48 | 24 | 24 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(38, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
38.3.f.a | $24$ | $1.035$ | None | \(0\) | \(-6\) | \(0\) | \(-18\) |
Decomposition of \(S_{3}^{\mathrm{old}}(38, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)