Properties

Label 3009.2.bi
Level 3009
Weight 2
Character orbit bi
Rep. character \(\chi_{3009}(19,\cdot)\)
Character field \(\Q(\zeta_{232})\)
Dimension 20160
Sturm bound 720

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Defining parameters

Level: \( N \) = \( 3009 = 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3009.bi (of order \(232\) and degree \(112\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 1003 \)
Character field: \(\Q(\zeta_{232})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3009, [\chi])\).

Total New Old
Modular forms 40768 20160 20608
Cusp forms 39872 20160 19712
Eisenstein series 896 0 896

Trace form

\( 20160q + O(q^{10}) \) \( 20160q + 32q^{14} + 720q^{16} + 16q^{17} - 16q^{19} - 32q^{22} - 16q^{23} - 64q^{26} + 16q^{29} - 32q^{31} + 80q^{32} - 32q^{33} + 32q^{34} - 64q^{35} - 16q^{37} - 32q^{39} + 48q^{40} + 32q^{41} + 32q^{42} + 32q^{43} - 32q^{46} - 864q^{50} + 96q^{52} + 16q^{53} - 80q^{56} + 32q^{57} - 48q^{58} - 16q^{59} - 96q^{61} + 64q^{65} + 32q^{66} - 496q^{67} + 80q^{68} + 64q^{69} + 64q^{70} + 496q^{71} + 32q^{73} - 96q^{74} - 32q^{75} + 128q^{76} - 160q^{77} - 64q^{78} + 16q^{80} + 16q^{82} - 48q^{85} + 128q^{86} - 48q^{87} - 64q^{88} + 32q^{91} + 224q^{92} - 32q^{93} - 16q^{94} - 64q^{95} - 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3009, [\chi])\) into irreducible Hecke orbits

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3009, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3009, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1003, [\chi])\)\(^{\oplus 2}\)