Properties

Label 2009.2.cl
Level $2009$
Weight $2$
Character orbit 2009.cl
Rep. character $\chi_{2009}(12,\cdot)$
Character field $\Q(\zeta_{840})$
Dimension $37248$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.cl (of order \(840\) and degree \(192\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{840})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 38016 38016 0
Cusp forms 37248 37248 0
Eisenstein series 768 768 0

Trace form

\( 37248q - 208q^{2} - 176q^{3} - 260q^{4} - 176q^{5} - 224q^{6} - 192q^{7} - 176q^{8} - 144q^{9} + O(q^{10}) \) \( 37248q - 208q^{2} - 176q^{3} - 260q^{4} - 176q^{5} - 224q^{6} - 192q^{7} - 176q^{8} - 144q^{9} - 132q^{10} - 208q^{11} - 176q^{12} - 224q^{13} - 188q^{14} - 136q^{15} + 596q^{16} - 140q^{17} - 72q^{18} - 264q^{19} - 224q^{20} - 232q^{21} - 208q^{22} - 260q^{23} - 56q^{24} - 260q^{25} - 144q^{26} - 224q^{27} - 208q^{28} - 144q^{29} - 152q^{30} - 360q^{31} - 196q^{32} - 116q^{33} - 224q^{34} - 248q^{35} - 112q^{36} - 192q^{37} - 92q^{38} - 208q^{39} - 224q^{41} - 160q^{43} + 1008q^{44} - 220q^{45} - 264q^{46} + 72q^{47} - 296q^{49} - 440q^{50} - 192q^{51} - 152q^{52} - 104q^{53} - 428q^{54} - 224q^{55} + 64q^{56} + 64q^{57} - 236q^{58} - 132q^{59} - 168q^{60} - 176q^{61} - 280q^{62} - 148q^{63} - 200q^{64} - 180q^{65} - 220q^{66} - 72q^{67} - 660q^{68} - 224q^{69} - 1084q^{70} - 80q^{71} - 260q^{72} - 128q^{73} - 164q^{74} - 812q^{75} + 1344q^{76} - 208q^{77} - 24q^{78} - 92q^{79} - 648q^{80} - 752q^{82} - 448q^{83} + 128q^{84} - 144q^{85} - 260q^{86} + 140q^{87} + 380q^{88} + 612q^{89} - 364q^{90} - 136q^{91} - 184q^{92} - 480q^{93} - 236q^{94} - 208q^{95} - 752q^{96} - 164q^{98} - 464q^{99} + O(q^{100}) \)

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

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