Defining parameters
Level: | \( N \) | \(=\) | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 168.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(64\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(168, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 36 | 12 | 24 |
Cusp forms | 28 | 12 | 16 |
Eisenstein series | 8 | 0 | 8 |
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.c.a | $4$ | $1.341$ | \(\Q(\zeta_{12})\) | None | \(2\) | \(0\) | \(0\) | \(-4\) | \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+\zeta_{12}^{2}q^{3}+(\zeta_{12}+\cdots)q^{4}+\cdots\) |
168.2.c.b | $8$ | $1.341$ | 8.0.386672896.3 | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q-\beta _{4}q^{2}-\beta _{2}q^{3}+\beta _{1}q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(168, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(168, [\chi]) \cong \)