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Properties

Label 231.4.n
Level $231$
Weight $4$
Character orbit 231.n
Rep. character $\chi_{231}(89,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 231.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(231, [\chi])\).

Total New Old
Modular forms 200 160 40
Cusp forms 184 160 24
Eisenstein series 16 0 16

Trace form

\( 160 q + 320 q^{4} + 92 q^{7} - 28 q^{9} + 330 q^{12} + 8 q^{15} - 1280 q^{16} - 54 q^{18} - 612 q^{19} - 572 q^{21} - 288 q^{24} - 2000 q^{25} + 1600 q^{28} + 1300 q^{30} + 1020 q^{31} - 1812 q^{36} - 1232 q^{37}+ \cdots + 7002 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(231, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
231.4.n.a 231.n 21.g $160$ $13.629$ None 231.4.n.a \(0\) \(0\) \(0\) \(92\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(231, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(231, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)