Defining parameters
Level: | \( N \) | \(=\) | \( 18 = 2 \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 18.d (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(21\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(18, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 12 | 28 |
Cusp forms | 32 | 12 | 20 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(18, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
18.7.d.a | $12$ | $4.141$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(-42\) | \(432\) | \(240\) | \(q-\beta _{3}q^{2}+(-6+4\beta _{1}+\beta _{2}-\beta _{3}+\beta _{7}+\cdots)q^{3}+\cdots\) |
Decomposition of \(S_{7}^{\mathrm{old}}(18, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(18, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)