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Properties

Label 231.4.bc
Level $231$
Weight $4$
Character orbit 231.bc
Rep. character $\chi_{231}(5,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $736$
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.bc (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{30})\)
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 800 800 0
Cusp forms 736 736 0
Eisenstein series 64 64 0

Trace form

\( 736 q - 9 q^{3} - 358 q^{4} - 51 q^{9} - 120 q^{10} + 24 q^{12} - 240 q^{15} + 1002 q^{16} - 83 q^{18} - 18 q^{19} - 162 q^{21} - 1032 q^{22} - 555 q^{24} + 2254 q^{25} - 56 q^{28} + 69 q^{30} - 1260 q^{31}+ \cdots + 11174 q^{99}+O(q^{100}) \) 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.bc.a 231.bc 231.ac $736$ $13.629$ None 231.4.bc.a \(0\) \(-9\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$