Properties

Label 168.2.bc
Level $168$
Weight $2$
Character orbit 168.bc
Rep. character $\chi_{168}(37,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 168.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
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 72 32 40
Cusp forms 56 32 24
Eisenstein series 16 0 16

Trace form

\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} + 16 q^{9} + 6 q^{10} + 22 q^{14} - 10 q^{16} - 2 q^{18} - 40 q^{20} - 12 q^{22} - 8 q^{23} - 6 q^{24} + 16 q^{25} + 6 q^{26} - 26 q^{28} - 8 q^{30} - 24 q^{31} - 8 q^{32}+ \cdots - 64 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(168, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
168.2.bc.a 168.bc 56.p $32$ $1.341$ None 168.2.bc.a \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(168, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(168, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)