Properties

Label 91.2.r
Level $91$
Weight $2$
Character orbit 91.r
Rep. character $\chi_{91}(25,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
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.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
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 24 0
Cusp forms 16 16 0
Eisenstein series 8 8 0

Trace form

\( 16q - 4q^{3} + 6q^{4} - 12q^{9} + O(q^{10}) \) \( 16q - 4q^{3} + 6q^{4} - 12q^{9} - 6q^{10} + 18q^{12} - 12q^{13} - 26q^{14} + 2q^{16} + 8q^{17} - 36q^{22} - 12q^{23} - 6q^{26} + 32q^{27} - 16q^{29} + 38q^{30} - 56q^{36} + 34q^{38} + 18q^{39} - 4q^{40} + 16q^{42} + 16q^{43} + 36q^{48} + 40q^{49} + 16q^{51} - 42q^{52} - 20q^{53} + 24q^{55} - 36q^{56} - 12q^{61} + 44q^{62} + 88q^{64} - 30q^{65} + 2q^{66} - 2q^{68} - 56q^{69} + 42q^{74} + 8q^{75} - 76q^{77} + 20q^{78} + 20q^{79} - 24q^{81} - 16q^{82} - 68q^{87} + 4q^{88} - 216q^{90} + 56q^{91} + 12q^{92} - 26q^{94} - 16q^{95} + O(q^{100}) \)

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.r.a \(16\) \(0.727\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{11}q^{2}+(-1+\beta _{3}+\beta _{6})q^{3}+(1+\cdots)q^{4}+\cdots\)