Properties

Label 168.2.t
Level 168
Weight 2
Character orbit 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

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

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.t.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