Properties

Label 2009.2.bd
Level $2009$
Weight $2$
Character orbit 2009.bd
Rep. character $\chi_{2009}(155,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $2328$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.bd (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2009 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 2376 2376 0
Cusp forms 2328 2328 0
Eisenstein series 48 48 0

Trace form

\( 2328q - 10q^{3} + 364q^{4} + 2q^{6} - 12q^{7} + O(q^{10}) \) \( 2328q - 10q^{3} + 364q^{4} + 2q^{6} - 12q^{7} - 44q^{10} - 18q^{11} - 6q^{12} - 10q^{13} - 10q^{14} - 10q^{15} - 412q^{16} + 2q^{17} - 64q^{18} - 16q^{19} + 6q^{22} - 20q^{23} - 50q^{24} + 352q^{25} - 58q^{26} - 4q^{27} + 48q^{28} + 58q^{29} - 32q^{30} - 208q^{31} - 58q^{34} - 52q^{35} - 28q^{37} + 82q^{38} - 20q^{40} - 58q^{41} - 264q^{42} - 62q^{44} + 44q^{45} - 84q^{47} + 12q^{48} + 4q^{51} + 62q^{52} + 20q^{53} + 52q^{54} + 16q^{55} - 94q^{56} - 48q^{57} + 50q^{58} - 28q^{59} + 70q^{60} + 26q^{63} + 332q^{64} + 34q^{65} + 164q^{66} - 40q^{67} - 28q^{68} - 58q^{69} - 116q^{70} + 48q^{71} + 120q^{72} - 114q^{75} - 212q^{76} + 212q^{78} + 4q^{79} + 56q^{81} - 2q^{82} - 28q^{83} - 22q^{85} - 52q^{86} - 240q^{88} - 118q^{89} - 76q^{92} - 98q^{93} - 176q^{94} - 32q^{95} + 166q^{96} - 140q^{97} - 24q^{98} - 80q^{99} + O(q^{100}) \)

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

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