↑

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 $392$

Related objects

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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

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