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

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

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.g.a \(2\) \(0.727\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-6\) \(-3\) \(-5\) \(q-\zeta_{6}q^{2}-3q^{3}+(1-\zeta_{6})q^{4}+(-3+\cdots)q^{5}+\cdots\)
91.2.g.b \(12\) \(0.727\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(-2\) \(1\) \(9\) \(q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}+(\beta _{3}-\beta _{11})q^{3}+\cdots\)