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Properties

Label 182.4.o
Level $182$
Weight $4$
Character orbit 182.o
Rep. character $\chi_{182}(23,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $56$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 182.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(182, [\chi])\).

Total New Old
Modular forms 176 56 120
Cusp forms 160 56 104
Eisenstein series 16 0 16

Trace form

\( 56 q - 224 q^{4} + 18 q^{7} - 220 q^{9} + 40 q^{10} + 42 q^{11} + 118 q^{13} + 16 q^{14} - 120 q^{15} + 896 q^{16} - 276 q^{17} - 192 q^{18} - 126 q^{19} + 168 q^{21} + 28 q^{22} + 280 q^{23} + 636 q^{25}+ \cdots - 5088 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(182, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
182.4.o.a 182.o 91.k $56$ $10.738$ None 182.4.o.a \(0\) \(0\) \(0\) \(18\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(182, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(182, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)