Properties

Label 2009.2.y
Level $2009$
Weight $2$
Character orbit 2009.y
Rep. character $\chi_{2009}(197,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1112$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.y (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 1632 1192 440
Cusp forms 1504 1112 392
Eisenstein series 128 80 48

Trace form

\( 1112 q + 10 q^{2} + 10 q^{3} + 276 q^{4} + 10 q^{5} + 30 q^{6} - 50 q^{8} + O(q^{10}) \) \( 1112 q + 10 q^{2} + 10 q^{3} + 276 q^{4} + 10 q^{5} + 30 q^{6} - 50 q^{8} + 42 q^{10} + 8 q^{11} + 14 q^{12} + 16 q^{13} - 24 q^{15} - 240 q^{16} + 12 q^{17} + 60 q^{18} + 24 q^{19} - 20 q^{20} - 58 q^{22} + 24 q^{23} + 40 q^{24} + 244 q^{25} + 8 q^{26} - 14 q^{27} - 104 q^{29} + 88 q^{30} - 8 q^{31} - 10 q^{33} + 48 q^{34} - 160 q^{36} - 2 q^{38} - 30 q^{39} + 108 q^{40} - 80 q^{43} + 104 q^{44} - 24 q^{45} - 110 q^{46} + 68 q^{47} - 70 q^{48} - 24 q^{51} - 36 q^{52} - 30 q^{53} - 16 q^{54} + 52 q^{55} - 118 q^{57} + 32 q^{58} + 42 q^{59} - 128 q^{60} - 30 q^{61} + 10 q^{62} + 230 q^{64} + 72 q^{65} - 58 q^{66} - 6 q^{67} + 100 q^{68} + 106 q^{69} - 120 q^{71} + 98 q^{72} + 30 q^{74} + 116 q^{75} + 124 q^{76} - 42 q^{78} - 6 q^{79} - 130 q^{80} - 884 q^{81} + 158 q^{82} - 40 q^{83} - 116 q^{85} - 66 q^{86} + 10 q^{87} - 114 q^{88} + 64 q^{89} + 70 q^{90} - 204 q^{92} - 38 q^{93} - 110 q^{94} - 48 q^{95} + 2 q^{96} + 22 q^{97} - 62 q^{99} + O(q^{100}) \)

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

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