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Properties

Label 2009.2.o
Level $2009$
Weight $2$
Character orbit 2009.o
Rep. character $\chi_{2009}(148,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $552$
Sturm bound $392$

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Defining parameters

Level: \( N \) \(=\) \( 2009 = 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2009.o (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(392\)

Dimensions

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

Total New Old
Modular forms 816 592 224
Cusp forms 752 552 200
Eisenstein series 64 40 24

Trace form

\( 552 q + 3 q^{2} - 129 q^{4} + q^{5} - 10 q^{6} - 4 q^{8} - 494 q^{9} + O(q^{10}) \) \( 552 q + 3 q^{2} - 129 q^{4} + q^{5} - 10 q^{6} - 4 q^{8} - 494 q^{9} - 30 q^{10} + 10 q^{11} - 10 q^{12} + 5 q^{13} - 50 q^{15} - 129 q^{16} + 10 q^{17} - 46 q^{18} - 10 q^{19} + 21 q^{20} - 45 q^{22} - 9 q^{23} - 70 q^{24} - 83 q^{25} + 20 q^{26} - 5 q^{29} + 90 q^{30} - 8 q^{31} - 20 q^{32} + 45 q^{33} - 50 q^{34} + 53 q^{36} + 60 q^{37} - 4 q^{39} + 72 q^{40} + 23 q^{41} - 29 q^{43} + 31 q^{45} + 34 q^{46} + 20 q^{47} - 20 q^{48} - 10 q^{50} + 71 q^{51} - 80 q^{52} - 20 q^{53} + 35 q^{54} - 12 q^{57} + 50 q^{58} - 3 q^{59} + 35 q^{61} + 20 q^{62} - 168 q^{64} - 80 q^{65} + 27 q^{66} - 70 q^{67} - 40 q^{71} + 90 q^{72} - 76 q^{73} + 54 q^{74} - 65 q^{75} + 165 q^{76} - 216 q^{78} + 10 q^{80} + 308 q^{81} + 89 q^{82} + 116 q^{83} - 59 q^{86} + 4 q^{87} - 50 q^{88} - 35 q^{89} + 164 q^{90} + 125 q^{92} + 60 q^{93} - 30 q^{94} - 95 q^{95} + 70 q^{97} - 35 q^{99} + O(q^{100}) \)

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

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