Properties

Label 91.2.h
Level $91$
Weight $2$
Character orbit 91.h
Rep. character $\chi_{91}(16,\cdot)$
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.h (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

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

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