Properties

Label 168.2.v
Level 168
Weight 2
Character orbit v
Rep. character \(\chi_{168}(11,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 56
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.v (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 168 \)
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 72 0
Cusp forms 56 56 0
Eisenstein series 16 16 0

Trace form

\( 56q - 2q^{3} - 2q^{4} - 8q^{6} - 2q^{9} + O(q^{10}) \) \( 56q - 2q^{3} - 2q^{4} - 8q^{6} - 2q^{9} + 6q^{10} + 10q^{12} - 10q^{16} - 10q^{18} - 4q^{19} - 20q^{22} - 8q^{24} - 16q^{25} - 8q^{27} - 22q^{28} - 12q^{30} - 14q^{33} - 56q^{34} + 4q^{36} + 14q^{40} - 8q^{42} - 16q^{43} - 12q^{46} + 64q^{48} - 16q^{49} - 34q^{51} - 8q^{52} + 32q^{54} + 4q^{57} - 18q^{58} + 40q^{60} + 4q^{64} - 20q^{66} - 36q^{67} - 42q^{70} + 22q^{72} + 4q^{73} + 104q^{76} + 28q^{78} - 10q^{81} + 52q^{82} + 4q^{84} + 46q^{88} + 140q^{90} + 72q^{91} - 46q^{96} - 32q^{97} - 44q^{99} + O(q^{100}) \)

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.v.a \(56\) \(1.341\) None \(0\) \(-2\) \(0\) \(0\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database