Properties

Label 2009.2.bb
Level $2009$
Weight $2$
Character orbit 2009.bb
Rep. character $\chi_{2009}(68,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $1088$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.bb (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{24})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 1632 1152 480
Cusp forms 1504 1088 416
Eisenstein series 128 64 64

Trace form

\( 1088q + 4q^{2} + 12q^{3} + 12q^{5} - 16q^{8} - 4q^{9} + O(q^{10}) \) \( 1088q + 4q^{2} + 12q^{3} + 12q^{5} - 16q^{8} - 4q^{9} + 24q^{10} + 4q^{11} + 12q^{12} - 56q^{15} + 504q^{16} - 24q^{17} + 8q^{18} - 12q^{19} + 80q^{22} + 60q^{24} + 36q^{26} - 80q^{29} - 20q^{30} - 40q^{32} - 48q^{33} + 32q^{36} - 16q^{37} - 72q^{38} + 4q^{39} + 64q^{43} - 84q^{44} - 20q^{46} - 12q^{47} + 120q^{50} - 16q^{51} - 12q^{52} + 44q^{53} + 180q^{54} - 80q^{57} + 80q^{58} + 24q^{59} + 44q^{60} + 12q^{61} - 72q^{65} + 12q^{67} + 84q^{68} - 48q^{71} + 48q^{73} + 8q^{74} - 168q^{75} + 64q^{78} + 120q^{80} - 132q^{82} - 400q^{85} + 144q^{87} + 32q^{88} - 36q^{89} - 224q^{92} + 68q^{93} - 96q^{94} + 4q^{95} - 12q^{96} - 144q^{99} + O(q^{100}) \)

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

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