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Properties

Label 2009.2.cb
Level $2009$
Weight $2$
Character orbit 2009.cb
Rep. character $\chi_{2009}(3,\cdot)$
Character field $\Q(\zeta_{168})$
Dimension $9312$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.cb (of order \(168\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{168})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 9504 9504 0
Cusp forms 9312 9312 0
Eisenstein series 192 192 0

Trace form

\( 9312 q - 52 q^{2} - 44 q^{3} - 44 q^{5} - 56 q^{6} - 48 q^{7} - 24 q^{8} - 116 q^{9} + O(q^{10}) \) \( 9312 q - 52 q^{2} - 44 q^{3} - 44 q^{5} - 56 q^{6} - 48 q^{7} - 24 q^{8} - 116 q^{9} - 88 q^{10} - 52 q^{11} - 44 q^{12} - 56 q^{13} - 52 q^{14} - 64 q^{15} - 856 q^{16} - 80 q^{17} - 48 q^{18} - 96 q^{19} - 56 q^{20} - 8 q^{21} + 8 q^{22} - 164 q^{24} - 76 q^{26} - 56 q^{27} - 32 q^{28} - 56 q^{29} - 8 q^{30} - 64 q^{32} - 104 q^{33} - 56 q^{34} - 32 q^{35} - 88 q^{36} - 128 q^{37} - 128 q^{38} - 52 q^{39} - 56 q^{41} + 480 q^{42} - 40 q^{43} + 292 q^{44} + 4 q^{46} + 128 q^{47} + 16 q^{49} - 40 q^{50} - 128 q^{51} - 68 q^{52} - 156 q^{53} + 208 q^{54} - 56 q^{55} - 304 q^{56} - 264 q^{57} - 24 q^{58} - 88 q^{59} - 92 q^{60} - 44 q^{61} - 92 q^{63} - 80 q^{65} - 48 q^{67} - 56 q^{69} - 356 q^{70} - 120 q^{71} - 92 q^{73} - 96 q^{74} + 112 q^{75} + 476 q^{76} + 48 q^{77} - 176 q^{78} - 28 q^{79} + 288 q^{80} - 188 q^{82} - 112 q^{83} - 168 q^{84} - 56 q^{85} - 360 q^{87} - 640 q^{88} + 48 q^{89} + 84 q^{90} + 56 q^{91} - 16 q^{92} + 220 q^{93} + 16 q^{94} - 52 q^{95} - 68 q^{96} + 24 q^{98} - 16 q^{99} + O(q^{100}) \)

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.