Defining parameters
Level: | \( N \) | \(=\) | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 168.j (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(64\) | ||
Trace bound: | \(2\) | ||
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 | 24 | 12 |
Cusp forms | 28 | 24 | 4 |
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.j.a | $4$ | $1.341$ | \(\Q(i, \sqrt{5})\) | None | \(-4\) | \(-2\) | \(4\) | \(0\) | \(q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\) |
168.2.j.b | $4$ | $1.341$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q-\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}+2q^{4}+2\zeta_{8}^{3}q^{5}+\cdots\) |
168.2.j.c | $4$ | $1.341$ | \(\Q(i, \sqrt{5})\) | None | \(4\) | \(-2\) | \(-4\) | \(0\) | \(q+(1+\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\) |
168.2.j.d | $12$ | $1.341$ | 12.0.\(\cdots\).2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{4}q^{2}-\beta _{6}q^{3}+(-\beta _{2}-\beta _{3})q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(168, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(168, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)