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

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

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

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