Properties

Label 168.2.bc
Level 168
Weight 2
Character orbit bc
Rep. character \(\chi_{168}(37,\cdot)\)
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.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

\( 32q + 2q^{2} - 2q^{4} - 16q^{8} + 16q^{9} + O(q^{10}) \) \( 32q + 2q^{2} - 2q^{4} - 16q^{8} + 16q^{9} + 6q^{10} + 22q^{14} - 10q^{16} - 2q^{18} - 40q^{20} - 12q^{22} - 8q^{23} - 6q^{24} + 16q^{25} + 6q^{26} - 26q^{28} - 8q^{30} - 24q^{31} - 8q^{32} - 24q^{34} - 4q^{36} - 26q^{38} - 6q^{40} - 4q^{42} + 20q^{44} + 16q^{46} - 24q^{47} - 16q^{48} + 8q^{49} + 52q^{50} + 44q^{52} - 64q^{55} + 40q^{56} - 16q^{57} + 34q^{58} - 22q^{60} + 100q^{62} - 20q^{64} + 12q^{66} + 16q^{68} + 38q^{70} - 80q^{71} - 8q^{72} + 8q^{73} + 10q^{74} - 32q^{76} + 12q^{78} + 8q^{79} - 56q^{80} - 16q^{81} - 16q^{84} - 22q^{86} + 24q^{87} + 50q^{88} + 12q^{90} + 64q^{92} - 48q^{94} + 24q^{95} + 10q^{96} - 48q^{97} - 64q^{98} + O(q^{100}) \)

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.bc.a \(32\) \(1.341\) None \(2\) \(0\) \(0\) \(0\)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database