Defining parameters
Level: | \( N \) | \(=\) | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 168.u (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(64\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(168, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80 | 16 | 64 |
Cusp forms | 48 | 16 | 32 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(168, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
168.2.u.a | $16$ | $1.341$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(4\) | \(q+(\beta _{3}+\beta _{9})q^{3}+\beta _{14}q^{5}-\beta _{10}q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(168, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(168, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 3}\)