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Properties

Label 931.2.ci
Level $931$
Weight $2$
Character orbit 931.ci
Rep. character $\chi_{931}(3,\cdot)$
Character field $\Q(\zeta_{126})$
Dimension $3276$
Newform subspaces $1$
Sturm bound $186$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.ci (of order \(126\) and degree \(36\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 931 \)
Character field: \(\Q(\zeta_{126})\)
Newform subspaces: \( 1 \)
Sturm bound: \(186\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(931, [\chi])\).

Total New Old
Modular forms 3420 3420 0
Cusp forms 3276 3276 0
Eisenstein series 144 144 0

Trace form

\( 3276 q - 39 q^{2} - 33 q^{3} - 39 q^{4} - 33 q^{5} - 42 q^{6} - 15 q^{7} - 45 q^{8} - 39 q^{9} + O(q^{10}) \) \( 3276 q - 39 q^{2} - 33 q^{3} - 39 q^{4} - 33 q^{5} - 42 q^{6} - 15 q^{7} - 45 q^{8} - 39 q^{9} - 6 q^{10} + 15 q^{11} - 66 q^{12} - 72 q^{13} - 18 q^{14} - 39 q^{15} - 45 q^{16} - 51 q^{17} - 87 q^{19} - 168 q^{20} - 36 q^{21} - 30 q^{22} - 39 q^{23} - 33 q^{24} - 39 q^{25} + 54 q^{26} - 51 q^{27} - 21 q^{28} - 42 q^{29} - 36 q^{30} - 108 q^{31} - 264 q^{32} - 33 q^{33} - 78 q^{34} + 45 q^{35} - 111 q^{36} - 36 q^{37} - 33 q^{38} - 96 q^{39} - 60 q^{40} + 12 q^{41} + 51 q^{42} - 54 q^{43} + 147 q^{44} - 126 q^{45} - 99 q^{46} - 33 q^{47} + 63 q^{48} - 39 q^{49} - 63 q^{50} - 39 q^{51} + 441 q^{52} - 3 q^{53} - 114 q^{54} - 87 q^{55} - 54 q^{56} + 24 q^{57} - 78 q^{58} - 42 q^{59} - 174 q^{60} - 57 q^{61} - 213 q^{62} - 57 q^{63} - 225 q^{64} - 63 q^{65} + 225 q^{66} - 54 q^{67} - 63 q^{69} - 66 q^{70} - 75 q^{71} - 519 q^{72} - 36 q^{73} - 57 q^{74} - 21 q^{75} + 12 q^{76} - 66 q^{77} + 531 q^{78} - 24 q^{79} - 90 q^{80} - 33 q^{81} - 93 q^{82} + 15 q^{83} - 162 q^{84} + 162 q^{85} + 126 q^{86} - 12 q^{87} - 63 q^{88} - 96 q^{89} - 291 q^{90} - 435 q^{91} - 36 q^{92} - 360 q^{93} - 540 q^{94} - 75 q^{95} + 567 q^{96} - 27 q^{97} - 111 q^{98} + 84 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(931, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
931.2.ci.a 931.ci 931.bi $3276$ $7.434$ None \(-39\) \(-33\) \(-33\) \(-15\) $\mathrm{SU}(2)[C_{126}]$