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Properties

Label 91.2.g
Level $91$
Weight $2$
Character orbit 91.g
Rep. character $\chi_{91}(9,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $14$
Newform subspaces $2$
Sturm bound $18$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(91, [\chi])\).

Total New Old
Modular forms 22 22 0
Cusp forms 14 14 0
Eisenstein series 8 8 0

Trace form

\( 14 q + q^{2} - 8 q^{3} - 3 q^{4} - 2 q^{5} - 6 q^{6} + 4 q^{7} - 12 q^{8} + 6 q^{9} + O(q^{10}) \) \( 14 q + q^{2} - 8 q^{3} - 3 q^{4} - 2 q^{5} - 6 q^{6} + 4 q^{7} - 12 q^{8} + 6 q^{9} - 2 q^{10} - 14 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{14} + 7 q^{15} + 9 q^{16} + 7 q^{17} - 3 q^{18} + 2 q^{20} + 6 q^{21} - 2 q^{22} - q^{23} + 40 q^{24} + 3 q^{25} - 26 q^{27} - 8 q^{28} - 4 q^{29} - 8 q^{30} + 13 q^{31} + 3 q^{32} - 14 q^{33} + 28 q^{34} + 11 q^{35} - 15 q^{36} - 15 q^{37} - 16 q^{38} - 17 q^{39} + 4 q^{40} - 11 q^{41} - 10 q^{42} - 4 q^{43} + 18 q^{44} - 25 q^{45} + 16 q^{46} - 2 q^{47} + 18 q^{48} + 8 q^{49} + 2 q^{50} - 26 q^{51} - 32 q^{52} - 5 q^{53} - 9 q^{54} + 18 q^{55} - 3 q^{56} + 48 q^{57} + 30 q^{58} + 17 q^{59} + 11 q^{60} - 16 q^{61} + 2 q^{62} + 2 q^{63} - 16 q^{64} + 40 q^{65} + 9 q^{66} + 16 q^{67} + 27 q^{68} + 23 q^{69} - 54 q^{70} - 7 q^{71} - 86 q^{72} - 17 q^{73} - 5 q^{74} + 9 q^{75} - 10 q^{76} + 26 q^{77} + 31 q^{78} + 10 q^{79} + 8 q^{80} + 30 q^{81} + 4 q^{82} - 54 q^{83} + 8 q^{84} + 5 q^{85} + 37 q^{87} + 18 q^{88} - 2 q^{89} + 20 q^{90} - 9 q^{91} + 54 q^{92} + 2 q^{93} - 88 q^{94} - 3 q^{95} + 34 q^{96} - 30 q^{97} + 49 q^{98} - 56 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(91, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
91.2.g.a 91.g 91.g $2$ $0.727$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-6\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}-3q^{3}+(1-\zeta_{6})q^{4}+(-3+\cdots)q^{5}+\cdots\)
91.2.g.b 91.g 91.g $12$ $0.727$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(-2\) \(1\) \(9\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}+(\beta _{3}-\beta _{11})q^{3}+\cdots\)