Properties

Label 2009.2.e
Level $2009$
Weight $2$
Character orbit 2009.e
Rep. character $\chi_{2009}(165,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $268$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 408 268 140
Cusp forms 376 268 108
Eisenstein series 32 0 32

Trace form

\( 268q + 4q^{2} + 2q^{3} - 132q^{4} - 2q^{5} - 8q^{6} - 24q^{8} - 128q^{9} + O(q^{10}) \) \( 268q + 4q^{2} + 2q^{3} - 132q^{4} - 2q^{5} - 8q^{6} - 24q^{8} - 128q^{9} - 4q^{10} + 14q^{11} - 6q^{12} + 8q^{13} - 40q^{15} - 120q^{16} + 8q^{17} + 18q^{18} + 6q^{19} + 32q^{20} - 32q^{22} + 16q^{23} + 32q^{24} - 152q^{25} + 20q^{26} + 8q^{27} - 40q^{29} - 12q^{30} - 6q^{31} + 18q^{32} - 20q^{33} + 32q^{34} + 184q^{36} - 12q^{37} + 18q^{39} + 20q^{40} - 16q^{41} + 80q^{43} + 42q^{44} - 18q^{45} + 48q^{46} + 6q^{47} + 100q^{48} - 20q^{50} + 8q^{51} - 26q^{52} - 4q^{53} + 38q^{54} - 40q^{55} + 8q^{57} + 40q^{58} - 34q^{59} + 116q^{60} - 14q^{61} - 20q^{62} + 64q^{64} + 72q^{65} + 8q^{66} + 26q^{67} + 18q^{68} - 24q^{69} - 112q^{71} + 70q^{72} + 64q^{74} + 22q^{75} - 32q^{76} - 76q^{78} + 24q^{79} - 92q^{80} - 86q^{81} + 4q^{82} + 32q^{83} + 36q^{85} - 56q^{86} + 30q^{87} + 40q^{88} + 16q^{89} - 8q^{90} - 12q^{92} - 82q^{93} - 4q^{94} + 6q^{95} + 106q^{96} - 44q^{97} - 136q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2009, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 2}\)