Properties

Label 668.2.b
Level $668$
Weight $2$
Character orbit 668.b
Rep. character $\chi_{668}(667,\cdot)$
Character field $\Q$
Dimension $82$
Newform subspaces $2$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 668 = 2^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 668.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 668 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(668, [\chi])\).

Total New Old
Modular forms 86 86 0
Cusp forms 82 82 0
Eisenstein series 4 4 0

Trace form

\( 82q - 2q^{2} + 2q^{4} - 8q^{6} - 8q^{8} - 82q^{9} + O(q^{10}) \) \( 82q - 2q^{2} + 2q^{4} - 8q^{6} - 8q^{8} - 82q^{9} + 18q^{12} + 10q^{14} + 10q^{16} - 20q^{18} + 20q^{22} + 10q^{24} - 78q^{25} + 4q^{29} + 18q^{32} + 8q^{33} + 30q^{36} - 36q^{38} + 3q^{42} - 5q^{44} + 27q^{48} - 82q^{49} - 40q^{50} + 3q^{54} + 50q^{56} + 8q^{57} - 22q^{58} + 36q^{61} + 5q^{62} + 8q^{64} + 24q^{65} + 24q^{66} - 31q^{72} - 36q^{76} + 114q^{81} + 33q^{84} - 16q^{85} - 20q^{88} + 28q^{89} + 72q^{93} + 90q^{94} + 2q^{96} - 4q^{97} + 51q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(668, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
668.2.b.a \(22\) \(5.334\) \(\Q(\sqrt{-167}) \) \(0\) \(0\) \(0\) \(0\)
668.2.b.b \(60\) \(5.334\) None \(-2\) \(0\) \(0\) \(0\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database