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Properties

Label 2006.2.g
Level $2006$
Weight $2$
Character orbit 2006.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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2006, [\chi])\) into newform subspaces

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

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