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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

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

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.