Properties

Label 2009.2.l
Level $2009$
Weight $2$
Character orbit 2009.l
Rep. character $\chi_{2009}(288,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $1128$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.l (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 1188 1128 60
Cusp forms 1164 1128 36
Eisenstein series 24 0 24

Trace form

\( 1128q - 4q^{3} - 192q^{4} - 4q^{5} - 4q^{6} - 12q^{7} - 192q^{9} + O(q^{10}) \) \( 1128q - 4q^{3} - 192q^{4} - 4q^{5} - 4q^{6} - 12q^{7} - 192q^{9} - 8q^{10} + 10q^{11} + 38q^{12} - 24q^{13} + 48q^{14} + 20q^{15} - 216q^{16} - 6q^{17} - 36q^{18} + 28q^{19} + 24q^{20} - 20q^{21} + 12q^{22} - 16q^{23} - 32q^{24} - 224q^{25} - 44q^{26} - 40q^{27} - 56q^{28} - 8q^{29} - 56q^{30} - 40q^{31} - 20q^{32} - 40q^{33} + 112q^{34} - 30q^{35} - 208q^{36} + 70q^{37} - 8q^{38} + 36q^{39} + 140q^{40} - 8q^{41} + 64q^{42} - 68q^{43} - 20q^{44} + 90q^{45} + 36q^{47} + 52q^{48} - 48q^{49} + 184q^{50} - 64q^{51} + 92q^{52} - 40q^{53} - 104q^{54} + 90q^{55} - 74q^{56} - 76q^{57} + 48q^{58} - 68q^{59} + 60q^{60} + 72q^{61} - 84q^{62} + 64q^{63} - 136q^{64} - 32q^{66} - 32q^{67} + 84q^{68} + 84q^{69} - 58q^{70} + 80q^{71} - 132q^{72} - 124q^{73} - 24q^{74} - 92q^{76} - 96q^{77} + 4q^{78} - 84q^{79} - 184q^{80} - 196q^{81} - 4q^{82} - 24q^{83} - 28q^{84} - 4q^{85} - 110q^{86} - 80q^{87} + 22q^{88} - 40q^{89} + 82q^{90} - 64q^{91} - 90q^{92} + 32q^{93} - 56q^{94} + 28q^{95} + 282q^{96} - 84q^{97} + 62q^{98} + 152q^{99} + O(q^{100}) \)

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

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