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Properties

Label 91.4.u
Level $91$
Weight $4$
Character orbit 91.u
Rep. character $\chi_{91}(30,\cdot)$
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.u (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

\( 52 q - 3 q^{2} - 14 q^{3} + 97 q^{4} - 6 q^{6} + 15 q^{7} + 426 q^{9} + 46 q^{10} - 112 q^{12} - 90 q^{13} - 116 q^{14} - 27 q^{15} - 299 q^{16} - 137 q^{17} - 321 q^{18} - 138 q^{20} + 3 q^{21} + 112 q^{22}+ \cdots - 597 q^{98}+O(q^{100}) \) 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.u.a 91.u 91.u $52$ $5.369$ None 91.4.k.a \(-3\) \(-14\) \(0\) \(15\) $\mathrm{SU}(2)[C_{6}]$