Properties

Label 2009.2.bp
Level $2009$
Weight $2$
Character orbit 2009.bp
Rep. character $\chi_{2009}(128,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $2176$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.bp (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 3264 2304 960
Cusp forms 3008 2176 832
Eisenstein series 256 128 128

Trace form

\( 2176q + 10q^{2} + 8q^{3} - 258q^{4} + 10q^{5} + 16q^{6} - 80q^{8} + O(q^{10}) \) \( 2176q + 10q^{2} + 8q^{3} - 258q^{4} + 10q^{5} + 16q^{6} - 80q^{8} - 18q^{10} + 12q^{11} + 24q^{12} + 32q^{13} - 64q^{15} + 262q^{16} + 2q^{17} - 42q^{18} + 4q^{19} - 80q^{20} - 80q^{22} + 6q^{23} - 26q^{24} - 234q^{25} + 18q^{26} + 92q^{27} + 24q^{29} - 10q^{30} + 38q^{31} - 100q^{33} + 56q^{34} - 6q^{38} + 10q^{39} - 20q^{40} + 44q^{41} - 160q^{43} + 28q^{44} + 106q^{45} - 90q^{46} - 32q^{47} + 20q^{48} + 72q^{51} + 20q^{52} + 46q^{53} - 72q^{54} + 16q^{55} - 88q^{57} - 34q^{58} - 54q^{59} + 42q^{60} + 90q^{61} + 40q^{62} + 416q^{64} - 46q^{65} - 22q^{66} + 32q^{67} + 42q^{68} - 24q^{69} - 20q^{71} - 94q^{72} + 10q^{74} + 32q^{75} - 348q^{76} - 208q^{78} - 14q^{79} + 90q^{80} + 792q^{81} + 124q^{82} - 432q^{83} - 156q^{85} + 86q^{86} + 10q^{87} + 250q^{88} + 50q^{89} - 80q^{90} - 36q^{92} - 4q^{93} + 50q^{94} + 140q^{95} + 64q^{96} + 4q^{97} + 220q^{99} + O(q^{100}) \)

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

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

Decomposition of \(S_{2}^{\mathrm{old}}(2009, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2009, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 2}\)