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Properties

Label 322.4.g
Level $322$
Weight $4$
Character orbit 322.g
Rep. character $\chi_{322}(45,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $2$
Sturm bound $192$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 322 = 2 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 322.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(322, [\chi])\).

Total New Old
Modular forms 296 96 200
Cusp forms 280 96 184
Eisenstein series 16 0 16

Trace form

\( 96 q - 192 q^{4} + 460 q^{9} - 768 q^{16} + 96 q^{18} + 70 q^{23} - 96 q^{24} - 1176 q^{25} + 216 q^{26} - 104 q^{29} + 264 q^{31} - 580 q^{35} - 3680 q^{36} + 68 q^{39} + 352 q^{46} - 1860 q^{47} + 1940 q^{49}+ \cdots + 848 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(322, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
322.4.g.a 322.g 161.g $48$ $18.999$ None 322.4.g.a \(-48\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
322.4.g.b 322.g 161.g $48$ $18.999$ None 322.4.g.b \(48\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(322, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(322, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)