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Properties

Label 133.2.ba
Level $133$
Weight $2$
Character orbit 133.ba
Rep. character $\chi_{133}(13,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $72$
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.ba (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 96 96 0
Cusp forms 72 72 0
Eisenstein series 24 24 0

Trace form

\( 72 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 12 q^{9} + O(q^{10}) \) \( 72 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 12 q^{9} - 12 q^{11} + 21 q^{14} - 18 q^{15} - 24 q^{16} - 12 q^{21} + 6 q^{23} - 18 q^{25} + 6 q^{28} - 42 q^{29} - 6 q^{30} + 60 q^{32} + 18 q^{35} - 90 q^{36} + 48 q^{39} + 81 q^{42} - 102 q^{43} - 18 q^{44} + 36 q^{46} + 18 q^{49} + 72 q^{50} - 12 q^{51} - 72 q^{53} + 108 q^{57} - 96 q^{58} - 78 q^{60} - 36 q^{63} + 30 q^{64} + 90 q^{65} - 18 q^{67} - 111 q^{70} + 48 q^{71} + 246 q^{72} + 54 q^{74} - 54 q^{77} - 78 q^{78} + 102 q^{79} + 42 q^{81} - 225 q^{84} + 24 q^{85} + 204 q^{86} - 18 q^{88} - 39 q^{91} + 30 q^{92} - 18 q^{93} - 48 q^{95} + 60 q^{98} + 12 q^{99} + O(q^{100}) \)

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.ba.a 133.ba 133.aa $72$ $1.062$ None \(-12\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$