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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

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

Display 100 coefficients 10 coefficients

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

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