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Properties

Label 3002.2.f
Level $3002$
Weight $2$
Character orbit 3002.f
Rep. character $\chi_{3002}(159,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $260$
Sturm bound $800$

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Defining parameters

Level: \( N \) \(=\) \( 3002 = 2 \cdot 19 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3002.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3002, [\chi])\).

Total New Old
Modular forms 808 260 548
Cusp forms 792 260 532
Eisenstein series 16 0 16

Trace form

\( 260 q + 2 q^{2} - 2 q^{3} - 130 q^{4} + 4 q^{5} - 2 q^{6} - 8 q^{7} - 4 q^{8} - 132 q^{9} + O(q^{10}) \) \( 260 q + 2 q^{2} - 2 q^{3} - 130 q^{4} + 4 q^{5} - 2 q^{6} - 8 q^{7} - 4 q^{8} - 132 q^{9} + 4 q^{10} + 4 q^{11} + 4 q^{12} + 20 q^{13} + 4 q^{14} - 8 q^{15} - 130 q^{16} - 8 q^{18} + 22 q^{19} - 8 q^{20} + 8 q^{21} - 14 q^{22} + 8 q^{23} - 2 q^{24} - 142 q^{25} - 8 q^{26} + 4 q^{27} + 4 q^{28} + 4 q^{29} + 16 q^{30} - 16 q^{31} + 2 q^{32} - 6 q^{33} + 12 q^{34} + 4 q^{35} - 132 q^{36} + 24 q^{37} - 8 q^{38} - 88 q^{39} + 4 q^{40} + 26 q^{41} + 12 q^{42} + 24 q^{43} - 2 q^{44} + 32 q^{45} - 40 q^{46} + 40 q^{47} - 2 q^{48} + 212 q^{49} - 12 q^{50} - 12 q^{51} + 20 q^{52} - 20 q^{53} + 34 q^{54} + 48 q^{55} - 8 q^{56} - 36 q^{57} + 8 q^{58} - 26 q^{59} - 8 q^{60} - 12 q^{62} + 16 q^{63} + 260 q^{64} - 96 q^{65} - 26 q^{66} - 26 q^{67} + 80 q^{69} - 8 q^{70} - 48 q^{71} + 4 q^{72} + 22 q^{73} + 40 q^{74} + 132 q^{75} + 10 q^{76} + 96 q^{77} + 4 q^{80} - 218 q^{81} - 14 q^{82} - 20 q^{83} - 16 q^{84} + 8 q^{85} + 24 q^{86} - 144 q^{87} + 28 q^{88} + 16 q^{89} + 52 q^{90} - 24 q^{91} + 8 q^{92} - 8 q^{93} - 72 q^{94} + 56 q^{95} + 4 q^{96} - 2 q^{97} - 14 q^{98} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3002, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3002, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3002, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1501, [\chi])\)\(^{\oplus 2}\)