Properties

Label 368.2.x
Level $368$
Weight $2$
Character orbit 368.x
Rep. character $\chi_{368}(11,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $920$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 368 = 2^{4} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 368.x (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 368 \)
Character field: \(\Q(\zeta_{44})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(368, [\chi])\).

Total New Old
Modular forms 1000 1000 0
Cusp forms 920 920 0
Eisenstein series 80 80 0

Trace form

\( 920 q - 18 q^{2} - 18 q^{3} - 22 q^{4} - 22 q^{5} - 12 q^{6} - 44 q^{7} - 18 q^{8} + O(q^{10}) \) \( 920 q - 18 q^{2} - 18 q^{3} - 22 q^{4} - 22 q^{5} - 12 q^{6} - 44 q^{7} - 18 q^{8} - 22 q^{10} - 22 q^{11} - 12 q^{12} - 18 q^{13} - 22 q^{14} - 6 q^{16} - 44 q^{17} - 46 q^{18} - 22 q^{19} - 22 q^{20} - 22 q^{21} - 48 q^{23} - 48 q^{24} + 2 q^{26} - 42 q^{27} - 22 q^{28} - 2 q^{29} - 22 q^{30} + 2 q^{32} - 44 q^{33} - 66 q^{34} - 38 q^{35} - 60 q^{36} - 22 q^{37} + 88 q^{38} - 12 q^{39} - 22 q^{40} - 242 q^{42} - 22 q^{43} - 22 q^{44} + 170 q^{46} - 78 q^{48} + 32 q^{49} - 184 q^{50} - 22 q^{51} + 50 q^{52} - 22 q^{53} + 102 q^{54} - 36 q^{55} - 22 q^{56} - 58 q^{58} - 30 q^{59} - 22 q^{60} - 22 q^{61} - 20 q^{62} - 64 q^{64} - 44 q^{65} - 22 q^{66} - 22 q^{67} + 2 q^{69} - 32 q^{70} - 36 q^{71} + 44 q^{72} - 22 q^{74} - 10 q^{75} - 22 q^{76} + 26 q^{77} - 56 q^{78} - 22 q^{80} + 24 q^{81} - 88 q^{82} - 22 q^{83} - 22 q^{84} - 6 q^{85} - 22 q^{86} - 36 q^{87} - 22 q^{88} - 22 q^{90} - 26 q^{92} - 292 q^{93} + 82 q^{94} - 46 q^{96} - 44 q^{97} + 66 q^{98} - 22 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(368, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
368.2.x.a 368.x 368.x $920$ $2.938$ None \(-18\) \(-18\) \(-22\) \(-44\) $\mathrm{SU}(2)[C_{44}]$