Properties

Label 2009.2.h
Level $2009$
Weight $2$
Character orbit 2009.h
Rep. character $\chi_{2009}(344,\cdot)$
Character field $\Q(\zeta_{5})$
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.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{5})\)
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

\( 552q + 5q^{2} + 10q^{3} - 129q^{4} + 5q^{5} + 8q^{6} - 28q^{8} + 514q^{9} + O(q^{10}) \) \( 552q + 5q^{2} + 10q^{3} - 129q^{4} + 5q^{5} + 8q^{6} - 28q^{8} + 514q^{9} - 2q^{11} + 28q^{12} + 17q^{13} - 18q^{15} - 113q^{16} + 8q^{17} - 2q^{18} - 6q^{19} - 21q^{20} - 5q^{22} + 21q^{23} - 6q^{24} - 119q^{25} - 18q^{26} + 46q^{27} + 19q^{29} - 70q^{30} - 8q^{31} - 56q^{32} + 49q^{33} + 10q^{34} - 121q^{36} - 4q^{37} - 86q^{38} - 14q^{39} - 20q^{40} - q^{41} - 3q^{43} + 116q^{44} - 7q^{45} + 44q^{46} - 20q^{47} - 74q^{48} - 54q^{50} + 17q^{51} + 16q^{52} + 36q^{53} + 25q^{54} - 12q^{55} + 14q^{57} - 12q^{58} + 21q^{59} + 96q^{60} + 39q^{61} + 30q^{62} - 124q^{64} + 6q^{65} + 19q^{66} + 36q^{67} - 42q^{68} - 2q^{69} - 40q^{71} - 88q^{72} + 32q^{73} - 132q^{74} + 61q^{75} - 29q^{76} - 26q^{78} - 62q^{79} - 96q^{80} + 416q^{81} + 7q^{82} + 76q^{83} - 106q^{85} - 7q^{86} - 66q^{87} + 76q^{88} + 61q^{89} + 42q^{90} - 109q^{92} - 18q^{93} - 32q^{94} + 43q^{95} + 214q^{96} - 14q^{97} + 93q^{99} + O(q^{100}) \)

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

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