Defining parameters
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
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: | \(20\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(38, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 102 | 30 | 72 |
Cusp forms | 78 | 30 | 48 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(38, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
38.4.e.a | $12$ | $2.242$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(-9\) | \(0\) | \(21\) | \(q-2\beta _{3}q^{2}+(-1+2\beta _{2}-\beta _{4}+2\beta _{6}+\cdots)q^{3}+\cdots\) |
38.4.e.b | $18$ | $2.242$ | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) | None | \(0\) | \(6\) | \(0\) | \(-33\) | \(q-2\beta _{8}q^{2}+(\beta _{3}+\beta _{4}+\beta _{6}+\beta _{9})q^{3}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(38, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)