Properties

Label 2009.2.z
Level $2009$
Weight $2$
Character orbit 2009.z
Rep. character $\chi_{2009}(247,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $2232$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.z (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 2376 2232 144
Cusp forms 2328 2232 96
Eisenstein series 48 0 48

Trace form

\( 2232q + 2q^{3} + 184q^{4} - 2q^{5} - 8q^{6} + 4q^{7} + 184q^{9} + O(q^{10}) \) \( 2232q + 2q^{3} + 184q^{4} - 2q^{5} - 8q^{6} + 4q^{7} + 184q^{9} - 4q^{10} - 16q^{11} - 76q^{12} + 8q^{13} - 72q^{14} - 20q^{15} + 172q^{16} - 6q^{17} - 18q^{18} - 50q^{19} - 24q^{20} - 12q^{22} - 8q^{23} + 32q^{24} + 168q^{25} + 20q^{26} + 8q^{27} - 36q^{28} + 8q^{29} - 28q^{30} - 6q^{31} - 10q^{32} - 20q^{33} - 136q^{34} - 30q^{35} - 352q^{36} - 42q^{37} + 56q^{38} + 4q^{39} + 76q^{40} - 16q^{41} - 166q^{42} + 40q^{43} - 94q^{44} + 66q^{45} - 78q^{47} + 212q^{48} + 40q^{49} - 184q^{50} - 32q^{51} + 86q^{52} - 20q^{53} + 38q^{54} - 12q^{55} - 10q^{56} + 48q^{57} - 144q^{58} - 34q^{59} + 156q^{60} - 56q^{61} + 36q^{62} - 124q^{63} - 424q^{64} + 8q^{66} - 2q^{67} - 150q^{68} - 192q^{69} - 62q^{70} - 80q^{71} - 66q^{72} - 12q^{74} - 62q^{75} - 32q^{76} + 24q^{77} - 4q^{78} - 28q^{79} - 92q^{80} + 266q^{81} + 4q^{82} + 144q^{83} + 140q^{84} + 4q^{85} - 34q^{86} + 2q^{87} - 94q^{88} + 16q^{89} + 440q^{90} + 54q^{91} + 48q^{92} + 282q^{93} - 4q^{94} + 182q^{95} + 330q^{96} + 68q^{97} + 292q^{98} - 152q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2009, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)