Properties

Label 368.2.w
Level $368$
Weight $2$
Character orbit 368.w
Rep. character $\chi_{368}(13,\cdot)$
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.w (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

\( 920q - 18q^{2} - 18q^{3} - 22q^{4} - 18q^{5} - 24q^{6} - 18q^{8} + O(q^{10}) \) \( 920q - 18q^{2} - 18q^{3} - 22q^{4} - 18q^{5} - 24q^{6} - 18q^{8} - 10q^{10} - 26q^{11} - 24q^{12} - 18q^{13} - 30q^{14} - 52q^{15} - 6q^{16} - 36q^{17} - 6q^{18} - 34q^{19} - 18q^{20} - 30q^{21} - 36q^{22} - 32q^{24} + 2q^{26} - 18q^{27} - 14q^{28} - 34q^{29} - 10q^{30} - 36q^{31} - 38q^{32} - 36q^{33} - 6q^{34} - 38q^{35} - 60q^{36} - 34q^{37} - 108q^{38} - 6q^{40} + 178q^{42} - 10q^{43} - 14q^{44} - 48q^{45} - 210q^{46} - 80q^{47} - 38q^{48} + 32q^{49} + 132q^{50} + 10q^{51} - 22q^{52} - 2q^{53} - 186q^{54} + 22q^{56} + 122q^{58} - 30q^{59} - 2q^{60} + 14q^{61} - 16q^{62} - 52q^{63} - 64q^{64} - 36q^{65} - 50q^{66} + 22q^{67} - 72q^{68} - 10q^{69} - 32q^{70} - 108q^{72} - 46q^{74} - 10q^{75} + 14q^{76} - 118q^{77} - 72q^{78} - 44q^{79} + 22q^{80} + 24q^{81} + 36q^{82} - 58q^{83} - 94q^{84} - 30q^{85} + 34q^{86} - 38q^{88} - 82q^{90} - 68q^{91} + 2q^{92} + 212q^{93} - 86q^{94} - 36q^{95} + 90q^{96} - 36q^{97} - 6q^{98} - 82q^{99} + O(q^{100}) \)

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.w.a \(920\) \(2.938\) None \(-18\) \(-18\) \(-18\) \(0\)