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Properties

Label 231.2.p
Level $231$
Weight $2$
Character orbit 231.p
Rep. character $\chi_{231}(10,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
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: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(231, [\chi])\).

Total New Old
Modular forms 72 32 40
Cusp forms 56 32 24
Eisenstein series 16 0 16

Trace form

\( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + O(q^{10}) \) \( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(231, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
231.2.p.a 231.p 77.i $32$ $1.845$ None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(231, [\chi])\) into lower level spaces

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