Properties

Label 91.2.k
Level $91$
Weight $2$
Character orbit 91.k
Rep. character $\chi_{91}(4,\cdot)$
Character field $\Q(\zeta_{6})$
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.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 14q - 2q^{3} - 10q^{4} - 6q^{6} - 7q^{7} + q^{9} + O(q^{10}) \) \( 14q - 2q^{3} - 10q^{4} - 6q^{6} - 7q^{7} + q^{9} + 9q^{10} + 3q^{11} - 2q^{12} - 4q^{13} + 10q^{14} - 9q^{15} + 6q^{16} - 22q^{17} - 3q^{18} + 6q^{19} - 6q^{20} + 16q^{21} - 6q^{22} - 6q^{23} + 18q^{24} - 7q^{25} + 6q^{26} + 22q^{27} - 5q^{28} - 4q^{29} + 14q^{30} + 15q^{31} - 15q^{33} - 9q^{35} - 15q^{36} + 16q^{38} - 11q^{39} - 4q^{40} - 15q^{41} - 11q^{42} - 24q^{44} + 14q^{48} - q^{49} + 24q^{50} + 10q^{51} - 5q^{52} + q^{53} - 24q^{55} + 33q^{56} - 15q^{58} - 33q^{60} - 2q^{61} + 38q^{62} - 28q^{63} + 24q^{65} - 43q^{66} + 30q^{67} + 10q^{68} + 7q^{69} + 18q^{70} + 33q^{71} + 51q^{72} + 57q^{73} + 66q^{74} - 6q^{75} - 42q^{76} - 10q^{77} + 47q^{78} - 30q^{79} - 78q^{80} + 13q^{81} - 4q^{82} - 7q^{84} - 3q^{85} - 90q^{86} - 26q^{87} - 5q^{88} - 12q^{90} - 15q^{91} - 66q^{92} - 14q^{94} - 10q^{95} + 12q^{96} - 12q^{97} - 42q^{98} + O(q^{100}) \)

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.k.a \(2\) \(0.727\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(-4\) \(q+(1-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(2-\zeta_{6})q^{5}+\cdots\)
91.2.k.b \(12\) \(0.727\) 12.0.\(\cdots\).1 None \(0\) \(-3\) \(-3\) \(-3\) \(q+\beta _{9}q^{2}+(\beta _{1}+\beta _{4}+\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)