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Properties

Label 2002.2.j
Level $2002$
Weight $2$
Character orbit 2002.j
Rep. character $\chi_{2002}(1145,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $160$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2002 = 2 \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2002.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2002, [\chi])\).

Total New Old
Modular forms 688 160 528
Cusp forms 656 160 496
Eisenstein series 32 0 32

Trace form

\( 160 q - 80 q^{4} - 8 q^{5} - 16 q^{6} - 72 q^{9} + O(q^{10}) \) \( 160 q - 80 q^{4} - 8 q^{5} - 16 q^{6} - 72 q^{9} + 16 q^{14} - 48 q^{15} - 80 q^{16} + 24 q^{17} + 16 q^{20} - 16 q^{21} - 8 q^{23} + 8 q^{24} - 88 q^{25} - 12 q^{26} + 72 q^{27} - 32 q^{29} + 20 q^{30} + 16 q^{31} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 144 q^{36} + 8 q^{37} + 16 q^{38} + 48 q^{41} + 40 q^{42} - 16 q^{43} + 8 q^{45} + 24 q^{46} + 8 q^{47} - 32 q^{49} - 32 q^{50} - 20 q^{51} - 32 q^{53} + 8 q^{54} - 8 q^{56} + 16 q^{57} + 8 q^{58} - 8 q^{59} + 24 q^{60} + 24 q^{61} - 24 q^{62} - 24 q^{63} + 160 q^{64} - 8 q^{65} + 8 q^{67} + 24 q^{68} - 40 q^{70} + 16 q^{71} - 16 q^{74} - 8 q^{77} - 24 q^{79} - 8 q^{80} - 80 q^{81} - 16 q^{82} + 64 q^{83} - 40 q^{84} - 32 q^{85} - 8 q^{86} + 24 q^{87} - 32 q^{89} - 120 q^{90} + 16 q^{92} + 16 q^{93} - 48 q^{94} - 8 q^{95} + 8 q^{96} + 16 q^{97} + 64 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2002, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2002, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2002, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1001, [\chi])\)\(^{\oplus 2}\)