Properties

Label 91.2.f
Level $91$
Weight $2$
Character orbit 91.f
Rep. character $\chi_{91}(22,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $3$
Sturm bound $18$
Trace bound $2$

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Defining parameters

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

\( 16q - 2q^{2} - 10q^{4} - 8q^{5} + 6q^{6} - 10q^{9} + O(q^{10}) \) \( 16q - 2q^{2} - 10q^{4} - 8q^{5} + 6q^{6} - 10q^{9} - 2q^{10} - 2q^{11} + 4q^{12} - 2q^{13} + 8q^{14} - 2q^{15} - 22q^{16} + 10q^{17} + 36q^{18} - 8q^{19} - 10q^{20} - 4q^{21} - 2q^{22} - 4q^{23} + 28q^{24} - 4q^{25} - 12q^{26} - 36q^{27} + 2q^{29} + 16q^{30} - 4q^{31} + 18q^{32} + 22q^{33} - 8q^{34} - 10q^{35} + 8q^{36} + 16q^{37} - 52q^{38} + 12q^{39} - 8q^{40} + 16q^{41} - 4q^{42} - 18q^{43} + 24q^{44} - 10q^{45} - 20q^{46} + 28q^{47} + 26q^{48} - 8q^{49} - 46q^{50} - 20q^{51} + 78q^{52} + 16q^{53} + 6q^{55} - 12q^{56} - 20q^{57} - 6q^{58} - 10q^{59} - 76q^{60} + 24q^{61} - 4q^{62} + 4q^{63} + 40q^{64} + 10q^{65} + 12q^{66} + 20q^{67} + 66q^{68} - 4q^{69} + 48q^{70} + 8q^{71} - 26q^{72} - 16q^{73} - 32q^{74} + 14q^{75} - 18q^{76} + 8q^{77} - 74q^{78} + 8q^{79} - 34q^{80} - 28q^{81} + 28q^{82} + 12q^{83} + 22q^{84} + 2q^{85} + 48q^{86} + 10q^{87} - 30q^{88} - 32q^{89} + 116q^{90} + 2q^{91} - 24q^{92} - 18q^{93} - 52q^{94} - 18q^{95} - 212q^{96} - 26q^{97} - 2q^{98} + 76q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
91.2.f.a \(4\) \(0.727\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-3\) \(3\) \(6\) \(-2\) \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+\cdots\)
91.2.f.b \(4\) \(0.727\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(-2\) \(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
91.2.f.c \(8\) \(0.727\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(-1\) \(-14\) \(4\) \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)