Properties

Label 392.3.s
Level $392$
Weight $3$
Character orbit 392.s
Rep. character $\chi_{392}(43,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $660$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 392.s (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 392 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(392, [\chi])\).

Total New Old
Modular forms 684 684 0
Cusp forms 660 660 0
Eisenstein series 24 24 0

Trace form

\( 660 q - 5 q^{2} - 10 q^{3} - 5 q^{4} + 3 q^{6} + q^{8} - 328 q^{9} + O(q^{10}) \) \( 660 q - 5 q^{2} - 10 q^{3} - 5 q^{4} + 3 q^{6} + q^{8} - 328 q^{9} + 5 q^{10} - 10 q^{11} + 38 q^{12} + 91 q^{14} + 19 q^{16} - 10 q^{17} - 36 q^{18} - 24 q^{19} + 45 q^{20} - 9 q^{22} - 147 q^{24} + 500 q^{25} - 59 q^{26} + 26 q^{27} - 252 q^{28} - 100 q^{30} + 35 q^{32} + 26 q^{33} - 61 q^{34} - 14 q^{35} + 25 q^{36} - 81 q^{38} + 245 q^{40} - 10 q^{41} + 63 q^{42} - 10 q^{43} + 181 q^{44} - 3 q^{46} - 100 q^{48} - 28 q^{49} - 240 q^{50} + 186 q^{51} - 83 q^{52} + 286 q^{54} - 588 q^{56} - 196 q^{57} + 205 q^{58} - 138 q^{59} - 599 q^{60} + 13 q^{62} - 227 q^{64} - 110 q^{65} + 105 q^{66} - 312 q^{67} + 376 q^{68} + 679 q^{70} + 158 q^{72} + 150 q^{73} + 129 q^{74} - 74 q^{75} - 418 q^{76} - 575 q^{78} - 516 q^{80} - 740 q^{81} + 842 q^{82} - 490 q^{83} - 1106 q^{84} + 137 q^{86} - 471 q^{88} - 106 q^{89} + 912 q^{90} + 658 q^{91} - 536 q^{92} - 766 q^{94} - 106 q^{96} + 232 q^{97} - 301 q^{98} + 336 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(392, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
392.3.s.a 392.s 392.s $660$ $10.681$ None \(-5\) \(-10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{14}]$