Properties

Label 168.2.t
Level $168$
Weight $2$
Character orbit 168.t
Rep. character $\chi_{168}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 168.t (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

\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9} + O(q^{10}) \) \( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9} - 18 q^{10} + 8 q^{11} - 10 q^{14} + 6 q^{16} + 2 q^{18} - 20 q^{22} - 18 q^{24} - 16 q^{25} - 30 q^{26} - 14 q^{28} - 8 q^{30} - 12 q^{32} - 24 q^{35} - 4 q^{36} - 18 q^{38} - 30 q^{40} + 4 q^{42} - 16 q^{43} + 24 q^{44} + 8 q^{46} + 8 q^{49} + 76 q^{50} + 36 q^{52} + 16 q^{56} + 16 q^{57} - 6 q^{58} - 96 q^{59} - 2 q^{60} + 76 q^{64} - 36 q^{66} - 32 q^{67} + 96 q^{68} + 6 q^{70} + 8 q^{72} - 24 q^{73} - 34 q^{74} - 12 q^{78} + 36 q^{80} - 16 q^{81} - 36 q^{82} + 16 q^{84} + 50 q^{86} - 14 q^{88} + 56 q^{91} - 128 q^{92} + 36 q^{94} + 30 q^{96} + 60 q^{98} + 16 q^{99} + O(q^{100}) \)

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

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

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

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