Properties

Label 91.2.bc
Level $91$
Weight $2$
Character orbit 91.bc
Rep. character $\chi_{91}(6,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $32$
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.bc (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 48 48 0
Cusp forms 32 32 0
Eisenstein series 16 16 0

Trace form

\( 32 q - 8 q^{2} - 12 q^{4} - 16 q^{8} + 8 q^{9} + O(q^{10}) \) \( 32 q - 8 q^{2} - 12 q^{4} - 16 q^{8} + 8 q^{9} - 4 q^{11} - 32 q^{14} - 8 q^{15} + 12 q^{16} - 4 q^{18} + 16 q^{21} + 4 q^{22} - 12 q^{23} + 24 q^{28} + 4 q^{29} + 12 q^{30} + 4 q^{32} - 20 q^{35} + 4 q^{37} - 36 q^{39} - 28 q^{42} - 48 q^{43} + 24 q^{44} + 84 q^{46} + 24 q^{49} - 44 q^{50} + 72 q^{53} + 60 q^{56} - 92 q^{57} - 16 q^{58} + 76 q^{60} + 48 q^{63} + 4 q^{65} - 56 q^{67} + 56 q^{70} + 84 q^{71} - 128 q^{72} - 24 q^{74} + 148 q^{78} - 80 q^{79} + 28 q^{81} - 64 q^{84} + 36 q^{85} - 48 q^{86} - 228 q^{88} - 48 q^{91} + 24 q^{92} + 108 q^{93} - 84 q^{95} - 32 q^{98} - 60 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(91, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
91.2.bc.a 91.bc 91.ac $32$ $0.727$ None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$