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Properties

Label 91.4.k
Level $91$
Weight $4$
Character orbit 91.k
Rep. character $\chi_{91}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $52$
Newform subspaces $1$
Sturm bound $37$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 91.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(37\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(91, [\chi])\).

Total New Old
Modular forms 60 60 0
Cusp forms 52 52 0
Eisenstein series 8 8 0

Trace form

\( 52 q + 7 q^{3} - 194 q^{4} - 6 q^{6} - 39 q^{7} - 213 q^{9} - 23 q^{10} - 45 q^{11} - 112 q^{12} - 90 q^{13} - 116 q^{14} - 27 q^{15} + 598 q^{16} + 274 q^{17} + 321 q^{18} + 9 q^{19} - 138 q^{20} - 3 q^{21}+ \cdots + 2220 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(91, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
91.4.k.a 91.k 91.k $52$ $5.369$ None 91.4.k.a \(0\) \(7\) \(0\) \(-39\) $\mathrm{SU}(2)[C_{6}]$