Properties

Label 2009.2.w
Level $2009$
Weight $2$
Character orbit 2009.w
Rep. character $\chi_{2009}(18,\cdot)$
Character field $\Q(\zeta_{15})$
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.w (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 1088q + 3q^{2} + 8q^{3} + 135q^{4} + 7q^{5} + 8q^{6} - 4q^{8} - 508q^{9} + O(q^{10}) \) \( 1088q + 3q^{2} + 8q^{3} + 135q^{4} + 7q^{5} + 8q^{6} - 4q^{8} - 508q^{9} + 24q^{10} - q^{11} - 19q^{12} + 12q^{13} - 30q^{15} + 123q^{16} - 3q^{17} + 36q^{18} - q^{19} + 48q^{20} + 56q^{22} + 18q^{24} + 147q^{25} - 15q^{26} - 28q^{27} - 88q^{29} + 87q^{30} + 11q^{31} + 2q^{32} - 10q^{33} + 108q^{34} - 406q^{36} + 40q^{37} + 10q^{38} + 2q^{39} - 70q^{40} + 6q^{41} - 32q^{43} + 20q^{44} - 12q^{45} + 58q^{46} - 31q^{47} - 110q^{48} - 120q^{50} + 52q^{51} - 69q^{52} + 14q^{53} - 43q^{54} + 80q^{55} + 2q^{57} - 31q^{58} + 29q^{59} - 136q^{60} + 9q^{61} - 30q^{62} - 272q^{64} - 22q^{65} - 78q^{66} - 13q^{67} + 42q^{68} - 46q^{69} - 42q^{71} + 53q^{72} - 30q^{73} - 11q^{74} - 52q^{75} - 118q^{76} + 246q^{78} + 2q^{79} + 17q^{80} - 456q^{81} + 21q^{82} + 208q^{83} - 116q^{85} - 53q^{86} - 10q^{87} - 24q^{88} + 89q^{89} - 242q^{90} - 86q^{92} - 53q^{93} - 81q^{94} + 59q^{95} + 64q^{96} + 24q^{97} + 184q^{99} + O(q^{100}) \)

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

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