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Properties

Label 92.5.g
Level $92$
Weight $5$
Character orbit 92.g
Rep. character $\chi_{92}(3,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $460$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 92 = 2^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 92.g (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 92 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(92, [\chi])\).

Total New Old
Modular forms 500 500 0
Cusp forms 460 460 0
Eisenstein series 40 40 0

Trace form

\( 460 q - 3 q^{2} - 43 q^{4} - 18 q^{5} - 44 q^{6} + 144 q^{8} + 1116 q^{9} - 77 q^{10} - 156 q^{12} - 18 q^{13} + 253 q^{14} - 795 q^{16} - 18 q^{17} - 676 q^{18} + 113 q^{20} + 266 q^{21} - 818 q^{22} + 1006 q^{24}+ \cdots + 52545 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(92, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
92.5.g.a 92.g 92.g $460$ $9.510$ None 92.5.g.a \(-3\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{22}]$