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Properties

Label 2000.2.cf
Level $2000$
Weight $2$
Character orbit 2000.cf
Rep. character $\chi_{2000}(3,\cdot)$
Character field $\Q(\zeta_{100})$
Dimension $11920$
Sturm bound $600$

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Defining parameters

Level: \( N \) \(=\) \( 2000 = 2^{4} \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2000.cf (of order \(100\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2000 \)
Character field: \(\Q(\zeta_{100})\)
Sturm bound: \(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2000, [\chi])\).

Total New Old
Modular forms 12080 12080 0
Cusp forms 11920 11920 0
Eisenstein series 160 160 0

Trace form

\( 11920 q - 40 q^{2} - 40 q^{3} - 40 q^{4} - 40 q^{5} - 40 q^{6} - 80 q^{7} - 40 q^{8} + O(q^{10}) \) \( 11920 q - 40 q^{2} - 40 q^{3} - 40 q^{4} - 40 q^{5} - 40 q^{6} - 80 q^{7} - 40 q^{8} - 40 q^{10} - 40 q^{11} - 40 q^{12} - 40 q^{13} - 40 q^{14} - 80 q^{17} - 40 q^{18} - 40 q^{19} - 40 q^{20} - 70 q^{21} - 90 q^{22} - 80 q^{23} - 50 q^{24} - 30 q^{26} - 40 q^{27} - 40 q^{28} - 40 q^{29} - 120 q^{30} - 40 q^{32} - 80 q^{33} - 40 q^{34} - 90 q^{35} - 40 q^{36} - 40 q^{37} - 40 q^{38} - 80 q^{39} - 90 q^{40} - 40 q^{42} - 50 q^{43} + 30 q^{44} - 40 q^{45} - 40 q^{46} - 170 q^{48} - 100 q^{49} + 30 q^{50} - 30 q^{51} - 50 q^{52} - 40 q^{53} - 10 q^{54} - 80 q^{55} - 40 q^{56} + 440 q^{58} - 40 q^{59} + 60 q^{60} - 40 q^{61} - 40 q^{62} - 70 q^{64} - 80 q^{65} - 40 q^{66} - 280 q^{67} - 40 q^{68} - 40 q^{69} - 40 q^{70} - 80 q^{71} + 110 q^{72} - 50 q^{74} - 40 q^{75} - 30 q^{76} + 30 q^{77} - 170 q^{78} - 800 q^{80} - 80 q^{81} - 80 q^{82} - 40 q^{83} - 40 q^{84} - 40 q^{85} - 160 q^{86} - 80 q^{87} - 40 q^{88} + 10 q^{90} + 30 q^{91} - 40 q^{92} - 50 q^{93} - 40 q^{94} - 200 q^{95} - 70 q^{96} - 80 q^{97} - 60 q^{98} - 50 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2000, [\chi])\) into newform subspaces

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