Properties

Label 91.2.w
Level $91$
Weight $2$
Character orbit 91.w
Rep. character $\chi_{91}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $28$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(91, [\chi])\).

Total New Old
Modular forms 44 44 0
Cusp forms 28 28 0
Eisenstein series 16 16 0

Trace form

\( 28q - 2q^{2} - 6q^{4} - 6q^{5} + 12q^{6} + 2q^{7} - 4q^{8} - 12q^{9} + O(q^{10}) \) \( 28q - 2q^{2} - 6q^{4} - 6q^{5} + 12q^{6} + 2q^{7} - 4q^{8} - 12q^{9} - 12q^{10} + 2q^{11} + 8q^{12} - 20q^{14} + 10q^{15} - 2q^{16} - 6q^{17} - 4q^{18} - 8q^{19} - 36q^{20} - 2q^{21} - 8q^{22} - 6q^{23} + 12q^{24} + 24q^{26} - 18q^{28} - 8q^{29} - 38q^{31} - 20q^{32} + 18q^{33} + 12q^{34} - 2q^{35} + 54q^{36} - 16q^{37} + 28q^{39} + 48q^{40} + 18q^{41} - 4q^{42} + 48q^{43} - 6q^{44} + 12q^{45} + 18q^{46} - 42q^{47} + 12q^{48} + 8q^{49} + 10q^{50} + 12q^{51} - 28q^{52} + 12q^{53} - 30q^{54} - 6q^{55} - 24q^{56} + 12q^{57} + 62q^{58} - 6q^{59} + 16q^{60} - 36q^{62} - 38q^{63} - 2q^{65} + 66q^{66} - 4q^{67} + 30q^{68} + 42q^{69} + 68q^{70} - 42q^{71} - 38q^{72} + 14q^{73} - 6q^{74} - 20q^{75} + 52q^{76} - 62q^{78} + 4q^{79} + 12q^{80} + 12q^{81} - 108q^{82} - 66q^{83} - 56q^{84} - 54q^{85} - 30q^{86} + 42q^{87} - 30q^{89} - 72q^{90} - 42q^{91} - 156q^{92} + 14q^{93} - 6q^{95} + 18q^{96} + 62q^{97} + 112q^{98} - 36q^{99} + O(q^{100}) \)

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.w.a \(28\) \(0.727\) None \(-2\) \(0\) \(-6\) \(2\)