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Properties

Label 2009.2.bz
Level $2009$
Weight $2$
Character orbit 2009.bz
Rep. character $\chi_{2009}(8,\cdot)$
Character field $\Q(\zeta_{140})$
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.bz (of order \(140\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{140})\)
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

\( 9312 q - 50 q^{2} - 40 q^{3} - 414 q^{4} - 50 q^{5} - 52 q^{6} - 48 q^{7} - 50 q^{8} + O(q^{10}) \) \( 9312 q - 50 q^{2} - 40 q^{3} - 414 q^{4} - 50 q^{5} - 52 q^{6} - 48 q^{7} - 50 q^{8} - 6 q^{10} - 32 q^{11} - 44 q^{12} - 40 q^{13} - 70 q^{14} - 40 q^{15} + 362 q^{16} - 52 q^{17} - 96 q^{18} - 104 q^{19} - 110 q^{20} - 60 q^{21} - 56 q^{22} - 30 q^{23} - 402 q^{25} + 8 q^{26} - 106 q^{27} - 158 q^{28} + 192 q^{29} - 48 q^{30} + 88 q^{31} - 90 q^{33} + 8 q^{34} + 12 q^{35} - 130 q^{36} - 42 q^{37} - 132 q^{38} - 50 q^{39} + 40 q^{40} - 52 q^{41} - 336 q^{42} - 50 q^{43} - 288 q^{44} - 194 q^{45} - 250 q^{46} - 116 q^{47} - 132 q^{48} - 40 q^{49} + 6 q^{51} - 112 q^{52} - 70 q^{53} - 182 q^{54} - 66 q^{55} - 106 q^{56} - 2 q^{57} - 100 q^{58} + 78 q^{59} - 360 q^{60} - 130 q^{61} - 50 q^{62} - 156 q^{63} - 422 q^{64} - 84 q^{65} + 286 q^{66} - 80 q^{67} + 8 q^{68} + 88 q^{69} - 604 q^{70} + 52 q^{71} - 330 q^{72} - 50 q^{74} + 224 q^{75} - 588 q^{76} - 50 q^{77} - 262 q^{78} - 124 q^{79} - 200 q^{80} + 1624 q^{81} + 192 q^{82} - 232 q^{83} - 40 q^{84} - 28 q^{85} + 2 q^{86} - 50 q^{87} + 190 q^{88} - 172 q^{89} + 70 q^{90} - 154 q^{92} + 48 q^{93} + 6 q^{94} - 18 q^{95} + 524 q^{96} + 100 q^{97} - 66 q^{98} - 220 q^{99} + O(q^{100}) \)

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.