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Properties

Label 2009.2.f
Level $2009$
Weight $2$
Character orbit 2009.f
Rep. character $\chi_{2009}(50,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $278$
Sturm bound $392$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 408 298 110
Cusp forms 376 278 98
Eisenstein series 32 20 12

Trace form

\( 278 q - 266 q^{4} - 10 q^{6} + O(q^{10}) \) \( 278 q - 266 q^{4} - 10 q^{6} + 8 q^{10} + 2 q^{11} - 4 q^{12} - 6 q^{13} - 6 q^{15} + 250 q^{16} - 2 q^{17} + 50 q^{18} + 16 q^{19} + 8 q^{22} - 4 q^{23} + 30 q^{24} - 234 q^{25} + 2 q^{26} - 6 q^{27} - 6 q^{29} - 58 q^{30} + 8 q^{31} - 38 q^{34} + 42 q^{38} - 28 q^{40} - 30 q^{41} - 34 q^{44} - 56 q^{45} + 12 q^{47} + 40 q^{48} + 24 q^{51} + 86 q^{52} + 30 q^{53} - 14 q^{54} - 2 q^{55} + 28 q^{57} - 22 q^{58} - 52 q^{59} + 18 q^{60} - 210 q^{64} + 8 q^{65} - 72 q^{66} - 14 q^{67} + 30 q^{68} - 36 q^{69} - 258 q^{72} + 44 q^{75} + 36 q^{76} - 8 q^{78} + 16 q^{79} - 166 q^{81} + 32 q^{82} - 20 q^{83} - 4 q^{85} - 4 q^{86} - 96 q^{88} - 34 q^{89} + 4 q^{92} - 72 q^{93} - 30 q^{94} + 58 q^{95} - 42 q^{96} + 58 q^{97} - 108 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2009, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(287, [\chi])\)\(^{\oplus 2}\)