Properties

Label 2009.2.s
Level $2009$
Weight $2$
Character orbit 2009.s
Rep. character $\chi_{2009}(214,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $544$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.s (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 816 576 240
Cusp forms 752 544 208
Eisenstein series 64 32 32

Trace form

\( 544q + 2q^{3} + 268q^{4} + 24q^{6} + O(q^{10}) \) \( 544q + 2q^{3} + 268q^{4} + 24q^{6} + 28q^{10} - 2q^{11} - 14q^{12} + 8q^{13} - 16q^{15} - 252q^{16} + 8q^{17} - 28q^{18} + 6q^{19} + 4q^{23} + 36q^{24} + 244q^{25} - 8q^{26} + 8q^{27} + 16q^{29} + 40q^{30} - 28q^{31} - 16q^{34} + 16q^{38} - 80q^{40} + 56q^{41} + 42q^{44} + 4q^{45} - 18q^{47} + 20q^{48} + 48q^{51} - 10q^{52} - 36q^{53} - 18q^{54} + 24q^{55} - 152q^{57} + 44q^{58} + 44q^{59} - 152q^{60} - 456q^{64} + 56q^{65} - 68q^{66} - 22q^{67} + 18q^{68} - 16q^{69} + 24q^{72} + 58q^{75} + 88q^{76} + 128q^{78} + 24q^{79} + 268q^{81} + 6q^{82} - 48q^{83} + 76q^{85} - 76q^{86} - 20q^{89} + 136q^{92} + 174q^{93} - 100q^{94} - 130q^{95} - 14q^{96} - 44q^{97} - 120q^{99} + O(q^{100}) \)

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

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