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Properties

Label 3006.2.f
Level $3006$
Weight $2$
Character orbit 3006.f
Rep. character $\chi_{3006}(1001,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $336$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 3006 = 2 \cdot 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3006.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1503 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3006, [\chi])\).

Total New Old
Modular forms 1016 336 680
Cusp forms 1000 336 664
Eisenstein series 16 0 16

Trace form

\( 336 q + 168 q^{4} + 8 q^{6} + 20 q^{9} + O(q^{10}) \) \( 336 q + 168 q^{4} + 8 q^{6} + 20 q^{9} + 24 q^{11} - 12 q^{14} - 168 q^{16} - 8 q^{18} + 44 q^{21} + 4 q^{24} - 168 q^{25} - 12 q^{27} + 12 q^{29} - 4 q^{33} + 16 q^{36} - 28 q^{42} - 180 q^{49} - 48 q^{50} + 16 q^{54} - 12 q^{56} - 36 q^{57} + 12 q^{61} - 16 q^{63} - 336 q^{64} - 24 q^{65} - 32 q^{66} + 8 q^{72} + 48 q^{75} + 36 q^{77} + 36 q^{81} - 20 q^{84} - 24 q^{85} + 4 q^{87} - 4 q^{93} + 12 q^{94} - 4 q^{96} + 112 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3006, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3006, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3006, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1503, [\chi])\)\(^{\oplus 2}\)