Properties

Label 2006.2.g
Level 2006
Weight 2
Character orbit g
Rep. character \(\chi_{2006}(355,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 352
Sturm bound 540

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Defining parameters

Level: \( N \) = \( 2006 = 2 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2006.g (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2006, [\chi])\).

Total New Old
Modular forms 1096 352 744
Cusp forms 1064 352 712
Eisenstein series 32 0 32

Trace form

\( 352q + 16q^{5} + O(q^{10}) \) \( 352q + 16q^{5} + 16q^{10} - 16q^{11} + 8q^{15} - 352q^{16} - 32q^{18} - 32q^{25} + 16q^{26} + 48q^{27} + 16q^{28} - 16q^{29} + 32q^{31} + 64q^{33} + 32q^{35} + 32q^{37} - 32q^{39} - 16q^{41} - 48q^{42} - 32q^{43} - 32q^{44} + 24q^{45} + 32q^{46} + 80q^{49} - 32q^{51} - 32q^{52} - 32q^{53} - 8q^{60} - 16q^{61} + 40q^{63} - 32q^{65} + 32q^{67} - 64q^{69} + 32q^{70} + 64q^{71} - 64q^{73} - 16q^{74} + 88q^{75} + 16q^{77} - 16q^{80} - 64q^{82} - 16q^{83} + 112q^{85} + 48q^{86} - 32q^{88} - 96q^{91} - 16q^{92} + 144q^{93} + 48q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2006, [\chi])\) into irreducible Hecke orbits

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

Decomposition of \(S_{2}^{\mathrm{old}}(2006, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2006, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1003, [\chi])\)\(^{\oplus 2}\)