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Properties

Label 133.2.w
Level $133$
Weight $2$
Character orbit 133.w
Rep. character $\chi_{133}(4,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $66$
Newform subspaces $1$
Sturm bound $26$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 133 = 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 133.w (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 1 \)
Sturm bound: \(26\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(133, [\chi])\).

Total New Old
Modular forms 90 90 0
Cusp forms 66 66 0
Eisenstein series 24 24 0

Trace form

\( 66 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 12 q^{6} - 9 q^{7} - 6 q^{8} - 3 q^{9} + O(q^{10}) \) \( 66 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 12 q^{6} - 9 q^{7} - 6 q^{8} - 3 q^{9} + 15 q^{10} - 54 q^{12} - 12 q^{13} - 3 q^{14} - 9 q^{15} + 9 q^{16} - 18 q^{18} + 6 q^{19} + 18 q^{21} - 12 q^{22} - 3 q^{23} - 36 q^{24} - 3 q^{25} - 18 q^{26} + 30 q^{27} + 45 q^{28} + 6 q^{29} + 3 q^{30} + 39 q^{31} + 6 q^{32} - 39 q^{33} - 24 q^{34} - 27 q^{35} + 51 q^{36} + 6 q^{37} - 72 q^{38} - 24 q^{39} + 57 q^{40} - 30 q^{41} + 87 q^{42} + 12 q^{43} - 48 q^{44} - 3 q^{45} - 12 q^{46} - 21 q^{47} - 21 q^{48} - 21 q^{49} + 27 q^{50} - 3 q^{51} - 9 q^{52} - 9 q^{53} + 93 q^{54} - 27 q^{55} + 12 q^{56} + 6 q^{57} - 42 q^{58} + 6 q^{59} + 48 q^{60} + 18 q^{61} - 27 q^{62} - 87 q^{63} + 24 q^{64} + 21 q^{65} + 15 q^{66} - 18 q^{67} - 15 q^{68} + 42 q^{69} + 15 q^{70} + 30 q^{71} + 48 q^{72} - 78 q^{73} + 21 q^{74} + 57 q^{75} + 42 q^{76} + 18 q^{77} - 51 q^{78} - 81 q^{79} - 3 q^{80} + 48 q^{81} + 117 q^{82} - 18 q^{83} - 51 q^{84} - 24 q^{85} - 66 q^{86} + 18 q^{87} - 45 q^{88} - 3 q^{89} - 48 q^{90} + 78 q^{91} + 12 q^{92} + 33 q^{93} + 72 q^{94} + 93 q^{95} + 69 q^{96} + 3 q^{97} + 6 q^{98} - 156 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(133, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
133.2.w.a 133.w 133.w $66$ $1.062$ None \(-3\) \(-3\) \(-3\) \(-9\) $\mathrm{SU}(2)[C_{9}]$