Defining parameters
Level: | \( N \) | \(=\) | \( 18 = 2 \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 18.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(27\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(18, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 28 | 4 | 24 |
Cusp forms | 20 | 4 | 16 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(18, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
18.9.b.a | $2$ | $7.333$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(-7064\) | \(q+8\beta q^{2}-2^{7}q^{4}+165\beta q^{5}-3532q^{7}+\cdots\) |
18.9.b.b | $2$ | $7.333$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(3304\) | \(q+8\beta q^{2}-2^{7}q^{4}-645\beta q^{5}+1652q^{7}+\cdots\) |
Decomposition of \(S_{9}^{\mathrm{old}}(18, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(18, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)