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Properties

Label 3006.2.m
Level $3006$
Weight $2$
Character orbit 3006.m
Rep. character $\chi_{3006}(7,\cdot)$
Character field $\Q(\zeta_{249})$
Dimension $27552$
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.m (of order \(249\) and degree \(164\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1503 \)
Character field: \(\Q(\zeta_{249})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 83312 27552 55760
Cusp forms 82000 27552 54448
Eisenstein series 1312 0 1312

Trace form

\( 27552 q + 168 q^{4} + 4 q^{5} - 8 q^{6} - 12 q^{9} + O(q^{10}) \) \( 27552 q + 168 q^{4} + 4 q^{5} - 8 q^{6} - 12 q^{9} - 8 q^{11} - 4 q^{14} + 20 q^{15} + 168 q^{16} + 8 q^{17} + 8 q^{18} + 4 q^{20} - 12 q^{21} - 12 q^{23} + 4 q^{24} + 168 q^{25} - 8 q^{26} + 36 q^{27} + 12 q^{29} - 20 q^{30} + 4 q^{33} - 32 q^{39} + 20 q^{41} - 12 q^{42} + 16 q^{44} + 56 q^{45} + 24 q^{46} + 156 q^{49} - 16 q^{50} - 28 q^{51} - 88 q^{53} + 16 q^{54} - 4 q^{56} - 12 q^{57} + 24 q^{59} - 16 q^{60} - 12 q^{61} + 48 q^{62} + 64 q^{63} - 336 q^{64} - 8 q^{65} - 4 q^{68} - 80 q^{69} - 12 q^{70} + 40 q^{71} + 8 q^{72} + 20 q^{74} - 32 q^{75} + 4 q^{77} + 32 q^{78} - 24 q^{79} - 8 q^{80} - 20 q^{81} - 24 q^{83} + 12 q^{84} - 24 q^{85} + 28 q^{86} - 20 q^{87} + 112 q^{89} + 8 q^{90} + 48 q^{91} - 12 q^{92} + 28 q^{93} - 12 q^{94} - 80 q^{95} + 4 q^{96} - 32 q^{98} + O(q^{100}) \)

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

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