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Properties

Label 231.4.ba
Level $231$
Weight $4$
Character orbit 231.ba
Rep. character $\chi_{231}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $384$
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.ba (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
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 800 384 416
Cusp forms 736 384 352
Eisenstein series 64 0 64

Trace form

\( 384 q - 172 q^{4} - 48 q^{5} - 20 q^{7} + 160 q^{8} - 432 q^{9} + 20 q^{11} - 312 q^{14} + 252 q^{15} + 892 q^{16} + 60 q^{17} + 90 q^{18} - 1320 q^{22} - 216 q^{23} + 1350 q^{24} - 1568 q^{25} + 912 q^{26}+ \cdots - 1440 q^{99}+O(q^{100}) \) 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.ba.a 231.ba 77.n $384$ $13.629$ None 231.4.ba.a \(0\) \(0\) \(-48\) \(-20\) $\mathrm{SU}(2)[C_{30}]$

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

\( S_{4}^{\mathrm{old}}(231, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)