Properties

Label 2009.2.cg
Level $2009$
Weight $2$
Character orbit 2009.cg
Rep. character $\chi_{2009}(6,\cdot)$
Character field $\Q(\zeta_{280})$
Dimension $18624$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.cg (of order \(280\) and degree \(96\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{280})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 19008 19008 0
Cusp forms 18624 18624 0
Eisenstein series 384 384 0

Trace form

\( 18624q - 80q^{2} - 112q^{3} - 100q^{4} - 112q^{5} - 112q^{6} - 96q^{7} - 64q^{8} - 120q^{9} + O(q^{10}) \) \( 18624q - 80q^{2} - 112q^{3} - 100q^{4} - 112q^{5} - 112q^{6} - 96q^{7} - 64q^{8} - 120q^{9} - 84q^{10} - 80q^{11} - 112q^{12} - 112q^{13} - 100q^{14} - 104q^{15} - 812q^{16} - 112q^{17} - 144q^{18} - 112q^{20} - 116q^{21} - 32q^{22} - 100q^{23} - 280q^{24} - 100q^{25} - 168q^{26} - 112q^{27} - 80q^{28} - 96q^{29} - 232q^{30} - 104q^{32} - 112q^{33} - 112q^{34} - 40q^{35} - 128q^{36} - 132q^{37} - 112q^{38} - 80q^{39} - 112q^{41} - 1152q^{42} - 80q^{43} + 432q^{44} - 140q^{45} - 144q^{46} - 504q^{47} - 64q^{49} - 136q^{50} - 132q^{51} - 112q^{52} - 40q^{53} - 28q^{54} - 112q^{55} - 268q^{56} - 244q^{57} - 136q^{58} - 84q^{59} - 112q^{61} - 56q^{62} - 224q^{63} - 100q^{64} - 24q^{65} - 140q^{66} - 144q^{67} - 112q^{69} + 976q^{70} - 160q^{71} - 100q^{72} - 196q^{73} - 40q^{74} + 224q^{75} - 1680q^{76} - 188q^{77} - 156q^{78} - 184q^{79} - 112q^{82} - 224q^{83} - 416q^{84} - 96q^{85} - 100q^{86} + 112q^{87} + 172q^{88} + 252q^{89} + 28q^{90} - 188q^{91} + 4q^{92} + 144q^{93} - 700q^{94} - 80q^{95} - 112q^{96} - 172q^{98} - 112q^{99} + O(q^{100}) \)

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

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