↑

Properties

Label 231.4.p
Level $231$
Weight $4$
Character orbit 231.p
Rep. character $\chi_{231}(10,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 231.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
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 96 104
Cusp forms 184 96 88
Eisenstein series 16 0 16

Trace form

\( 96 q + 172 q^{4} + 48 q^{5} + 432 q^{9} - 20 q^{11} + 272 q^{14} + 168 q^{15} - 492 q^{16} + 60 q^{22} + 216 q^{23} + 1748 q^{25} - 912 q^{26} - 828 q^{31} - 54 q^{33} + 3096 q^{36} + 52 q^{37} + 1488 q^{38}+ \cdots - 360 q^{99}+O(q^{100}) \) 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.p.a 231.p 77.i $96$ $13.629$ None 231.4.p.a \(0\) \(0\) \(48\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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