Properties

Label 667.2.f
Level $667$
Weight $2$
Character orbit 667.f
Rep. character $\chi_{667}(505,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $116$
Newform subspaces $2$
Sturm bound $120$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 667 = 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 667.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 667 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 124 124 0
Cusp forms 116 116 0
Eisenstein series 8 8 0

Trace form

\( 116q - 8q^{2} - 4q^{3} + 2q^{8} + O(q^{10}) \) \( 116q - 8q^{2} - 4q^{3} + 2q^{8} + 10q^{12} - 152q^{16} + 30q^{18} - 16q^{23} + 96q^{24} + 108q^{25} + 10q^{26} - 28q^{27} - 28q^{29} - 16q^{31} - 24q^{32} - 12q^{36} + 24q^{39} - 28q^{41} - 8q^{46} - 28q^{47} - 2q^{48} - 124q^{49} - 40q^{50} + 24q^{52} + 140q^{54} + 32q^{55} - 34q^{58} + 24q^{59} - 32q^{69} + 40q^{70} + 38q^{72} - 28q^{73} - 44q^{75} + 20q^{77} - 8q^{78} + 20q^{81} + 12q^{85} - 40q^{87} - 4q^{94} - 88q^{95} + 152q^{98} + O(q^{100}) \)

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.f.a \(12\) \(5.326\) 12.0.\(\cdots\).1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{9}-\beta _{10})q^{2}+(-\beta _{3}+\beta _{8}+\cdots)q^{3}+\cdots\)
667.2.f.b \(104\) \(5.326\) None \(-8\) \(-4\) \(0\) \(0\)