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

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

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

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