Properties

Label 667.2.q
Level $667$
Weight $2$
Character orbit 667.q
Rep. character $\chi_{667}(17,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $1160$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 667 = 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 667.q (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(\zeta_{44})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(667, [\chi])\).

Total New Old
Modular forms 1240 1240 0
Cusp forms 1160 1160 0
Eisenstein series 80 80 0

Trace form

\( 1160q - 14q^{2} - 18q^{3} - 44q^{7} - 24q^{8} + O(q^{10}) \) \( 1160q - 14q^{2} - 18q^{3} - 44q^{7} - 24q^{8} - 22q^{10} - 22q^{11} - 32q^{12} - 22q^{14} - 22q^{15} + 108q^{16} - 22q^{17} - 52q^{18} - 44q^{19} - 44q^{20} + 44q^{21} - 28q^{23} + 80q^{24} - 64q^{25} - 76q^{26} - 60q^{27} - 16q^{29} - 44q^{30} - 6q^{31} - 42q^{32} - 32q^{36} - 22q^{37} + 42q^{39} - 22q^{40} + 6q^{41} - 110q^{43} - 220q^{44} + 162q^{46} - 16q^{47} + 112q^{48} + 80q^{49} - 136q^{50} - 68q^{52} - 44q^{53} - 96q^{54} + 78q^{55} - 264q^{56} + 122q^{58} - 68q^{59} - 22q^{60} - 22q^{61} - 44q^{65} + 88q^{66} + 10q^{69} - 84q^{70} - 126q^{72} - 38q^{73} + 22q^{75} - 22q^{76} - 20q^{77} - 300q^{78} - 22q^{79} - 64q^{81} - 44q^{82} + 88q^{83} + 110q^{84} - 78q^{85} - 246q^{87} + 132q^{88} - 154q^{89} + 22q^{90} - 40q^{94} - 110q^{95} - 154q^{97} + 90q^{98} + 242q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(667, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
667.2.q.a \(1160\) \(5.326\) None \(-14\) \(-18\) \(0\) \(-44\)