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Properties

Label 669.2.k
Level $669$
Weight $2$
Character orbit 669.k
Rep. character $\chi_{669}(26,\cdot)$
Character field $\Q(\zeta_{74})$
Dimension $2592$
Newform subspaces $1$
Sturm bound $149$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 669 = 3 \cdot 223 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 669.k (of order \(74\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 669 \)
Character field: \(\Q(\zeta_{74})\)
Newform subspaces: \( 1 \)
Sturm bound: \(149\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(669, [\chi])\).

Total New Old
Modular forms 2736 2736 0
Cusp forms 2592 2592 0
Eisenstein series 144 144 0

Trace form

\( 2592 q - 37 q^{3} - 2 q^{4} - 37 q^{6} - 82 q^{7} - 33 q^{9} + O(q^{10}) \) \( 2592 q - 37 q^{3} - 2 q^{4} - 37 q^{6} - 82 q^{7} - 33 q^{9} - 74 q^{10} + 74 q^{12} - 74 q^{13} - 17 q^{15} - 138 q^{16} + 52 q^{18} - 54 q^{19} - 37 q^{21} - 74 q^{22} - 259 q^{24} - 142 q^{25} - 37 q^{27} - 26 q^{28} - 49 q^{30} - 98 q^{31} - 37 q^{33} - 74 q^{34} - 21 q^{36} - 70 q^{37} - 76 q^{39} - 37 q^{42} - 46 q^{43} - 37 q^{45} - 74 q^{46} - 37 q^{48} - 122 q^{49} - 37 q^{51} - 74 q^{52} - 37 q^{54} - 50 q^{55} - 148 q^{57} + 78 q^{58} - 75 q^{60} - 74 q^{61} - 45 q^{63} + 6 q^{64} - 15 q^{66} - 74 q^{67} - 21 q^{69} - 222 q^{70} + 41 q^{72} - 98 q^{73} - 259 q^{75} - 102 q^{76} + 89 q^{78} + 370 q^{79} - q^{81} + 14 q^{82} - 37 q^{84} - 222 q^{85} + 481 q^{87} - 74 q^{88} - 740 q^{90} - 74 q^{91} - 74 q^{93} - 174 q^{94} + 481 q^{96} - 74 q^{97} - 37 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(669, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
669.2.k.a 669.k 669.k $2592$ $5.342$ None \(0\) \(-37\) \(0\) \(-82\) $\mathrm{SU}(2)[C_{74}]$