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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
667.2.f.a 667.f 667.f $12$ $5.326$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(\beta _{1}-\beta _{9}-\beta _{10})q^{2}+(-\beta _{3}+\beta _{8}+\cdots)q^{3}+\cdots\)
667.2.f.b 667.f 667.f $104$ $5.326$ None \(-8\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$