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Properties

Label 91.2.e
Level $91$
Weight $2$
Character orbit 91.e
Rep. character $\chi_{91}(53,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $3$
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
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 24 16 8
Cusp forms 16 16 0
Eisenstein series 8 0 8

Trace form

\( 16 q - 2 q^{2} - 10 q^{4} - 2 q^{5} - 6 q^{7} - 4 q^{9} + O(q^{10}) \) \( 16 q - 2 q^{2} - 10 q^{4} - 2 q^{5} - 6 q^{7} - 4 q^{9} + 10 q^{10} - 2 q^{11} + 10 q^{12} + 4 q^{13} - 10 q^{14} - 20 q^{15} - 22 q^{16} + 4 q^{17} - 8 q^{19} + 32 q^{20} + 2 q^{21} + 28 q^{22} + 8 q^{23} - 20 q^{24} - 4 q^{25} - 6 q^{26} + 30 q^{28} - 16 q^{29} - 2 q^{30} - 4 q^{31} - 12 q^{32} - 8 q^{33} - 32 q^{34} - 4 q^{35} + 32 q^{36} - 8 q^{37} + 26 q^{38} - 8 q^{40} + 28 q^{41} + 32 q^{42} - 24 q^{43} + 6 q^{44} + 32 q^{45} - 20 q^{46} - 2 q^{47} - 76 q^{48} - 20 q^{49} + 8 q^{50} + 28 q^{51} - 6 q^{52} - 8 q^{53} - 18 q^{54} - 32 q^{57} + 42 q^{58} - 10 q^{59} + 44 q^{60} + 12 q^{61} - 76 q^{62} + 40 q^{63} + 40 q^{64} - 2 q^{65} - 6 q^{66} - 4 q^{67} + 18 q^{68} + 56 q^{69} + 54 q^{70} + 20 q^{71} + 22 q^{72} - 22 q^{73} + 34 q^{74} + 20 q^{75} + 48 q^{76} - 52 q^{77} - 20 q^{78} - 4 q^{79} - 70 q^{80} + 32 q^{81} - 44 q^{82} + 12 q^{83} - 98 q^{84} - 4 q^{85} - 54 q^{86} + 28 q^{87} - 24 q^{88} + 4 q^{89} - 88 q^{90} + 8 q^{91} - 12 q^{92} - 18 q^{93} - 46 q^{94} + 12 q^{95} + 22 q^{96} - 68 q^{97} + 34 q^{98} + 16 q^{99} + O(q^{100}) \)

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.e.a 91.e 7.c $2$ $0.727$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(2-3\zeta_{6})q^{7}+\cdots\)
91.2.e.b 91.e 7.c $4$ $0.727$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(3\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{3})q^{2}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{3}+\cdots\)
91.2.e.c 91.e 7.c $10$ $0.727$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-4\) \(0\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{7})q^{2}+(-\beta _{4}+\beta _{9})q^{3}+(-2+\cdots)q^{4}+\cdots\)