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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

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

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

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