Properties

Label 2009.2.bx
Level 2009
Weight 2
Character orbit bx
Rep. character \(\chi_{2009}(19,\cdot)\)
Character field \(\Q(\zeta_{120})\)
Dimension 4352
Sturm bound 392

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Defining parameters

Level: \( N \) = \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2009.bx (of order \(120\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 287 \)
Character field: \(\Q(\zeta_{120})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 6528 4608 1920
Cusp forms 6016 4352 1664
Eisenstein series 512 256 256

Trace form

\( 4352q + 16q^{2} + 48q^{3} + 20q^{4} + 48q^{5} - 144q^{8} + 24q^{9} + O(q^{10}) \) \( 4352q + 16q^{2} + 48q^{3} + 20q^{4} + 48q^{5} - 144q^{8} + 24q^{9} + 36q^{10} + 16q^{11} + 48q^{12} - 104q^{15} - 484q^{16} + 84q^{17} + 12q^{18} + 72q^{19} - 240q^{22} + 20q^{23} + 20q^{25} + 24q^{26} - 80q^{29} + 60q^{31} + 60q^{32} + 108q^{33} - 192q^{36} - 24q^{37} + 132q^{38} + 16q^{39} - 224q^{43} - 16q^{44} + 60q^{45} + 40q^{46} + 72q^{47} - 280q^{50} - 24q^{51} + 72q^{52} - 24q^{53} - 120q^{54} - 80q^{57} - 60q^{58} + 36q^{59} - 24q^{60} + 48q^{61} - 160q^{64} + 92q^{65} + 60q^{66} + 8q^{67} - 324q^{68} - 112q^{71} + 20q^{72} + 12q^{73} + 12q^{74} - 252q^{75} - 224q^{78} + 20q^{79} - 60q^{80} - 528q^{82} + 240q^{85} + 20q^{86} - 84q^{87} - 12q^{88} - 144q^{89} + 64q^{92} - 48q^{93} + 156q^{94} + 16q^{95} - 528q^{96} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2009, [\chi])\) into irreducible Hecke orbits

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

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