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

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

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

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