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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
368.2.x.a \(920\) \(2.938\) None \(-18\) \(-18\) \(-22\) \(-44\)