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Properties

Label 2009.2.bp
Level $2009$
Weight $2$
Character orbit 2009.bp
Rep. character $\chi_{2009}(128,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $2176$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.bp (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 3264 2304 960
Cusp forms 3008 2176 832
Eisenstein series 256 128 128

Trace form

\( 2176 q + 10 q^{2} + 8 q^{3} - 258 q^{4} + 10 q^{5} + 16 q^{6} - 80 q^{8} + O(q^{10}) \) \( 2176 q + 10 q^{2} + 8 q^{3} - 258 q^{4} + 10 q^{5} + 16 q^{6} - 80 q^{8} - 18 q^{10} + 12 q^{11} + 24 q^{12} + 32 q^{13} - 64 q^{15} + 262 q^{16} + 2 q^{17} - 42 q^{18} + 4 q^{19} - 80 q^{20} - 80 q^{22} + 6 q^{23} - 26 q^{24} - 234 q^{25} + 18 q^{26} + 92 q^{27} + 24 q^{29} - 10 q^{30} + 38 q^{31} - 100 q^{33} + 56 q^{34} - 6 q^{38} + 10 q^{39} - 20 q^{40} + 44 q^{41} - 160 q^{43} + 28 q^{44} + 106 q^{45} - 90 q^{46} - 32 q^{47} + 20 q^{48} + 72 q^{51} + 20 q^{52} + 46 q^{53} - 72 q^{54} + 16 q^{55} - 88 q^{57} - 34 q^{58} - 54 q^{59} + 42 q^{60} + 90 q^{61} + 40 q^{62} + 416 q^{64} - 46 q^{65} - 22 q^{66} + 32 q^{67} + 42 q^{68} - 24 q^{69} - 20 q^{71} - 94 q^{72} + 10 q^{74} + 32 q^{75} - 348 q^{76} - 208 q^{78} - 14 q^{79} + 90 q^{80} + 792 q^{81} + 124 q^{82} - 432 q^{83} - 156 q^{85} + 86 q^{86} + 10 q^{87} + 250 q^{88} + 50 q^{89} - 80 q^{90} - 36 q^{92} - 4 q^{93} + 50 q^{94} + 140 q^{95} + 64 q^{96} + 4 q^{97} + 220 q^{99} + O(q^{100}) \)

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

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