Properties

Label 2009.2.cb
Level $2009$
Weight $2$
Character orbit 2009.cb
Rep. character $\chi_{2009}(3,\cdot)$
Character field $\Q(\zeta_{168})$
Dimension $9312$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.cb (of order \(168\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{168})\)
Sturm bound: \(392\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2009, [\chi])\).

Total New Old
Modular forms 9504 9504 0
Cusp forms 9312 9312 0
Eisenstein series 192 192 0

Trace form

\( 9312q - 52q^{2} - 44q^{3} - 44q^{5} - 56q^{6} - 48q^{7} - 24q^{8} - 116q^{9} + O(q^{10}) \) \( 9312q - 52q^{2} - 44q^{3} - 44q^{5} - 56q^{6} - 48q^{7} - 24q^{8} - 116q^{9} - 88q^{10} - 52q^{11} - 44q^{12} - 56q^{13} - 52q^{14} - 64q^{15} - 856q^{16} - 80q^{17} - 48q^{18} - 96q^{19} - 56q^{20} - 8q^{21} + 8q^{22} - 164q^{24} - 76q^{26} - 56q^{27} - 32q^{28} - 56q^{29} - 8q^{30} - 64q^{32} - 104q^{33} - 56q^{34} - 32q^{35} - 88q^{36} - 128q^{37} - 128q^{38} - 52q^{39} - 56q^{41} + 480q^{42} - 40q^{43} + 292q^{44} + 4q^{46} + 128q^{47} + 16q^{49} - 40q^{50} - 128q^{51} - 68q^{52} - 156q^{53} + 208q^{54} - 56q^{55} - 304q^{56} - 264q^{57} - 24q^{58} - 88q^{59} - 92q^{60} - 44q^{61} - 92q^{63} - 80q^{65} - 48q^{67} - 56q^{69} - 356q^{70} - 120q^{71} - 92q^{73} - 96q^{74} + 112q^{75} + 476q^{76} + 48q^{77} - 176q^{78} - 28q^{79} + 288q^{80} - 188q^{82} - 112q^{83} - 168q^{84} - 56q^{85} - 360q^{87} - 640q^{88} + 48q^{89} + 84q^{90} + 56q^{91} - 16q^{92} + 220q^{93} + 16q^{94} - 52q^{95} - 68q^{96} + 24q^{98} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2009, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.