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Properties

Label 91.2.q
Level $91$
Weight $2$
Character orbit 91.q
Rep. character $\chi_{91}(36,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $12$
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.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
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 24 12 12
Cusp forms 16 12 4
Eisenstein series 8 0 8

Trace form

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

Display 100 coefficients 10 coefficients

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.q.a \(12\) \(0.727\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{4}-\beta _{6}+\beta _{10})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(91, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(91, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)