Defining parameters
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.c (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(40\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(38, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 74 | 26 | 48 |
Cusp forms | 66 | 26 | 40 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(38, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
38.8.c.a | $12$ | $11.871$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(-48\) | \(12\) | \(124\) | \(-1036\) | \(q+8\beta _{2}q^{2}+(\beta _{1}-2\beta _{2})q^{3}+(-2^{6}-2^{6}\beta _{2}+\cdots)q^{4}+\cdots\) |
38.8.c.b | $14$ | $11.871$ | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) | None | \(56\) | \(55\) | \(-126\) | \(1928\) | \(q+8\beta _{3}q^{2}+(\beta _{1}+\beta _{2}+8\beta _{3})q^{3}+(-2^{6}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{8}^{\mathrm{old}}(38, [\chi])\) into lower level spaces
\( S_{8}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)