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Properties

Label 2009.2.bu
Level $2009$
Weight $2$
Character orbit 2009.bu
Rep. character $\chi_{2009}(9,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $4656$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.bu (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 4752 4752 0
Cusp forms 4656 4656 0
Eisenstein series 96 96 0

Trace form

\( 4656 q - 26 q^{3} - 436 q^{4} - 32 q^{6} - 24 q^{7} + O(q^{10}) \) \( 4656 q - 26 q^{3} - 436 q^{4} - 32 q^{6} - 24 q^{7} - 28 q^{10} - 30 q^{11} - 42 q^{12} - 20 q^{13} - 38 q^{14} - 20 q^{15} + 316 q^{16} - 20 q^{17} - 8 q^{18} - 8 q^{19} - 36 q^{22} - 52 q^{23} + 92 q^{24} - 424 q^{25} - 8 q^{26} - 62 q^{27} - 84 q^{28} - 88 q^{29} - 34 q^{30} + 112 q^{31} - 44 q^{34} - 2 q^{35} - 56 q^{37} - 40 q^{38} - 136 q^{40} + 28 q^{41} - 96 q^{42} - 202 q^{44} - 164 q^{45} - 60 q^{47} - 36 q^{48} - 40 q^{51} - 38 q^{52} - 158 q^{53} + 164 q^{54} - 46 q^{55} + 274 q^{56} - 12 q^{57} + 88 q^{58} + 100 q^{59} - 280 q^{60} - 38 q^{63} + 688 q^{64} - 4 q^{65} - 404 q^{66} - 20 q^{67} + 4 q^{68} - 44 q^{69} + 134 q^{70} - 78 q^{71} - 492 q^{72} + 198 q^{75} + 326 q^{76} - 272 q^{78} + 2 q^{79} + 40 q^{81} - 22 q^{82} - 104 q^{83} - 8 q^{85} - 68 q^{86} - 360 q^{88} - 188 q^{89} + 16 q^{92} + 122 q^{93} - 352 q^{94} - 112 q^{95} - 154 q^{96} + 68 q^{97} + 60 q^{98} + 8 q^{99} + O(q^{100}) \)

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.