Defining parameters
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
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: | \(50\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(38, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 282 | 90 | 192 |
Cusp forms | 258 | 90 | 168 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(38, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
38.10.e.a | $42$ | $19.571$ | None | \(0\) | \(-252\) | \(0\) | \(14373\) | ||
38.10.e.b | $48$ | $19.571$ | None | \(0\) | \(33\) | \(0\) | \(-25809\) |
Decomposition of \(S_{10}^{\mathrm{old}}(38, [\chi])\) into lower level spaces
\( S_{10}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)