Defining parameters
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.e (of order \(9\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q(\zeta_{9})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(30\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(38, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 162 | 54 | 108 |
Cusp forms | 138 | 54 | 84 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(38, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
38.6.e.a | $24$ | $6.095$ | None | \(0\) | \(18\) | \(0\) | \(438\) | ||
38.6.e.b | $30$ | $6.095$ | None | \(0\) | \(15\) | \(0\) | \(-84\) |
Decomposition of \(S_{6}^{\mathrm{old}}(38, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)