Properties

Label 91.2.k
Level $91$
Weight $2$
Character orbit 91.k
Rep. character $\chi_{91}(4,\cdot)$
Character field $\Q(\zeta_{6})$
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.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 14 q - 2 q^{3} - 10 q^{4} - 6 q^{6} - 7 q^{7} + q^{9} + O(q^{10}) \) \( 14 q - 2 q^{3} - 10 q^{4} - 6 q^{6} - 7 q^{7} + q^{9} + 9 q^{10} + 3 q^{11} - 2 q^{12} - 4 q^{13} + 10 q^{14} - 9 q^{15} + 6 q^{16} - 22 q^{17} - 3 q^{18} + 6 q^{19} - 6 q^{20} + 16 q^{21} - 6 q^{22} - 6 q^{23} + 18 q^{24} - 7 q^{25} + 6 q^{26} + 22 q^{27} - 5 q^{28} - 4 q^{29} + 14 q^{30} + 15 q^{31} - 15 q^{33} - 9 q^{35} - 15 q^{36} + 16 q^{38} - 11 q^{39} - 4 q^{40} - 15 q^{41} - 11 q^{42} - 24 q^{44} + 14 q^{48} - q^{49} + 24 q^{50} + 10 q^{51} - 5 q^{52} + q^{53} - 24 q^{55} + 33 q^{56} - 15 q^{58} - 33 q^{60} - 2 q^{61} + 38 q^{62} - 28 q^{63} + 24 q^{65} - 43 q^{66} + 30 q^{67} + 10 q^{68} + 7 q^{69} + 18 q^{70} + 33 q^{71} + 51 q^{72} + 57 q^{73} + 66 q^{74} - 6 q^{75} - 42 q^{76} - 10 q^{77} + 47 q^{78} - 30 q^{79} - 78 q^{80} + 13 q^{81} - 4 q^{82} - 7 q^{84} - 3 q^{85} - 90 q^{86} - 26 q^{87} - 5 q^{88} - 12 q^{90} - 15 q^{91} - 66 q^{92} - 14 q^{94} - 10 q^{95} + 12 q^{96} - 12 q^{97} - 42 q^{98} + O(q^{100}) \)

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.k.a 91.k 91.k $2$ $0.727$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(2-\zeta_{6})q^{5}+\cdots\)
91.2.k.b 91.k 91.k $12$ $0.727$ 12.0.\(\cdots\).1 None \(0\) \(-3\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{9}q^{2}+(\beta _{1}+\beta _{4}+\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)