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Properties

Label 133.2.bf
Level $133$
Weight $2$
Character orbit 133.bf
Rep. character $\chi_{133}(10,\cdot)$
Character field $\Q(\zeta_{18})$
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.bf (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 133 \)
Character field: \(\Q(\zeta_{18})\)
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

\( 66 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 18 q^{8} - 3 q^{9} + O(q^{10}) \) \( 66 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 18 q^{8} - 3 q^{9} - 9 q^{10} - 12 q^{11} + 6 q^{12} - 30 q^{13} - 15 q^{14} + 9 q^{15} - 15 q^{16} + 18 q^{17} + 36 q^{18} + 12 q^{19} - 30 q^{21} - 3 q^{23} - 36 q^{24} - 27 q^{25} + 12 q^{27} - 33 q^{28} - 6 q^{29} + 3 q^{30} - 9 q^{31} + 60 q^{32} - 9 q^{33} - 36 q^{34} + 9 q^{35} + 27 q^{36} - 36 q^{37} + 18 q^{38} + 12 q^{39} + 9 q^{40} + 54 q^{41} - 9 q^{42} + 12 q^{43} + 18 q^{44} - 27 q^{45} + 45 q^{47} + 63 q^{48} - 45 q^{49} - 63 q^{50} - 3 q^{51} + 57 q^{52} + 27 q^{53} - 9 q^{54} - 45 q^{55} - 54 q^{56} - 54 q^{57} + 30 q^{58} + 36 q^{59} - 78 q^{60} - 42 q^{61} - 45 q^{62} + 57 q^{63} - 36 q^{64} + 45 q^{65} + 9 q^{66} + 30 q^{67} - 9 q^{68} + 69 q^{70} - 6 q^{71} - 6 q^{72} + 60 q^{73} + 9 q^{74} - 21 q^{75} + 54 q^{76} - 18 q^{77} + 3 q^{78} + 27 q^{79} - 45 q^{80} + 24 q^{81} - 9 q^{82} + 36 q^{83} + 99 q^{84} - 48 q^{85} - 48 q^{86} - 9 q^{88} - 9 q^{89} - 18 q^{90} + 24 q^{91} + 48 q^{92} - 3 q^{93} + 90 q^{94} - 75 q^{95} + 63 q^{96} - 27 q^{97} + 96 q^{98} + 48 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
133.2.bf.a 133.bf 133.af $66$ $1.062$ None 133.2.bb.a \(-3\) \(-9\) \(-9\) \(3\) $\mathrm{SU}(2)[C_{18}]$