Properties

Label 2009.2.cj
Level $2009$
Weight $2$
Character orbit 2009.cj
Rep. character $\chi_{2009}(2,\cdot)$
Character field $\Q(\zeta_{420})$
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.cj (of order \(420\) and degree \(96\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{420})\)
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

\( 18624q - 130q^{2} - 104q^{3} + 306q^{4} - 130q^{5} - 68q^{6} - 96q^{7} - 100q^{8} + O(q^{10}) \) \( 18624q - 130q^{2} - 104q^{3} + 306q^{4} - 130q^{5} - 68q^{6} - 96q^{7} - 100q^{8} - 102q^{10} - 100q^{11} - 88q^{12} - 80q^{13} - 122q^{14} - 80q^{15} - 446q^{16} - 110q^{17} - 12q^{18} - 52q^{19} - 220q^{20} - 120q^{21} - 64q^{22} - 78q^{23} - 222q^{24} + 294q^{25} - 122q^{26} + 22q^{27} + 14q^{28} - 312q^{29} - 6q^{30} - 172q^{31} - 240q^{33} - 56q^{34} - 138q^{35} - 20q^{36} - 84q^{37} - 90q^{38} - 130q^{39} - 244q^{40} - 68q^{41} + 336q^{42} - 100q^{43} - 708q^{44} + 134q^{45} - 230q^{46} + 80q^{47} - 204q^{48} - 140q^{49} - 60q^{51} - 92q^{52} + 28q^{53} - 394q^{54} - 54q^{55} - 254q^{56} - 88q^{57} - 218q^{58} + 30q^{59} + 30q^{60} - 50q^{61} - 100q^{62} - 12q^{63} - 748q^{64} - 126q^{65} - 526q^{66} - 40q^{67} - 14q^{68} - 136q^{69} + 226q^{70} - 172q^{71} + 282q^{72} - 130q^{74} - 248q^{75} + 324q^{76} - 220q^{77} + 172q^{78} - 62q^{79} + 20q^{80} - 2080q^{81} + 12q^{82} - 656q^{83} - 140q^{84} - 92q^{85} - 62q^{86} - 130q^{87} + 230q^{88} - 482q^{89} - 220q^{90} + 64q^{92} - 252q^{93} + 162q^{94} - 18q^{95} - 776q^{96} - 388q^{97} - 150q^{98} - 68q^{99} + O(q^{100}) \)

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

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