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Properties

Label 2008.2.n
Level $2008$
Weight $2$
Character orbit 2008.n
Rep. character $\chi_{2008}(149,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1000$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 2008 = 2^{3} \cdot 251 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2008.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2008 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2008, [\chi])\).

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

Trace form

\( 1000 q - 8 q^{2} - 8 q^{4} + 3 q^{6} - 6 q^{7} - 8 q^{8} + 240 q^{9} + O(q^{10}) \) \( 1000 q - 8 q^{2} - 8 q^{4} + 3 q^{6} - 6 q^{7} - 8 q^{8} + 240 q^{9} + 8 q^{10} + 21 q^{12} - 11 q^{14} + 12 q^{15} - 16 q^{16} - 6 q^{17} - 19 q^{18} + 46 q^{20} + 15 q^{22} - 6 q^{23} + 71 q^{24} - 984 q^{25} - 29 q^{26} - 19 q^{28} - 3 q^{30} - 6 q^{31} + 12 q^{32} - 10 q^{33} - 23 q^{34} - 7 q^{36} + 26 q^{38} - 18 q^{39} + 54 q^{40} - 14 q^{41} - 45 q^{42} - 3 q^{44} - 53 q^{46} - 96 q^{47} - 24 q^{48} - 244 q^{49} + 10 q^{50} + 55 q^{52} - 93 q^{54} + 8 q^{55} - 24 q^{56} - 26 q^{57} - 26 q^{58} + 4 q^{60} - 21 q^{62} - 40 q^{63} + 4 q^{64} + 24 q^{65} - 50 q^{66} + 26 q^{68} + 21 q^{70} - 82 q^{71} - 25 q^{72} - 6 q^{73} - 52 q^{74} - 13 q^{76} - 37 q^{78} - 6 q^{79} + 30 q^{80} - 244 q^{81} + 35 q^{82} + 20 q^{84} + 13 q^{86} - 126 q^{87} - 33 q^{88} - 6 q^{89} + 9 q^{90} - 68 q^{92} - 46 q^{94} + 56 q^{95} + 8 q^{96} + 10 q^{97} + 104 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2008, [\chi])\) into newform subspaces

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