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Properties

Label 731.2.j
Level $731$
Weight $2$
Character orbit 731.j
Rep. character $\chi_{731}(135,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
Newform subspaces $1$
Sturm bound $132$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 731 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(132\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(731, [\chi])\).

Total New Old
Modular forms 136 136 0
Cusp forms 128 128 0
Eisenstein series 8 8 0

Trace form

\( 128 q - 4 q^{2} + 116 q^{4} - 12 q^{8} + 70 q^{9} + O(q^{10}) \) \( 128 q - 4 q^{2} + 116 q^{4} - 12 q^{8} + 70 q^{9} + 4 q^{13} - 12 q^{15} + 76 q^{16} + 2 q^{17} - 16 q^{18} - 2 q^{19} - 20 q^{21} + 60 q^{25} - 2 q^{26} - 28 q^{30} - 48 q^{32} + 22 q^{33} - 18 q^{34} - 112 q^{35} + 36 q^{36} - 40 q^{38} + 36 q^{42} + 10 q^{43} + 36 q^{47} + 52 q^{49} + 16 q^{50} + 10 q^{51} + 10 q^{52} + 24 q^{55} - 12 q^{59} - 78 q^{60} + 36 q^{64} + 14 q^{66} + 10 q^{67} - q^{68} - 64 q^{70} - 68 q^{72} - 22 q^{76} - 28 q^{77} - 20 q^{81} - 6 q^{83} + 32 q^{84} + 6 q^{85} - 58 q^{86} + 32 q^{87} + 36 q^{89} + 6 q^{93} + 132 q^{94} - 48 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(731, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
731.2.j.a 731.j 731.j $128$ $5.837$ None 731.2.j.a \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$