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Properties

Label 2005.2.bk
Level $2005$
Weight $2$
Character orbit 2005.bk
Rep. character $\chi_{2005}(48,\cdot)$
Character field $\Q(\zeta_{80})$
Dimension $6368$
Sturm bound $402$

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Defining parameters

Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.bk (of order \(80\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2005 \)
Character field: \(\Q(\zeta_{80})\)
Sturm bound: \(402\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2005, [\chi])\).

Total New Old
Modular forms 6496 6496 0
Cusp forms 6368 6368 0
Eisenstein series 128 128 0

Trace form

\( 6368 q - 32 q^{2} - 40 q^{3} - 24 q^{5} - 64 q^{6} - 32 q^{7} - 16 q^{8} + O(q^{10}) \) \( 6368 q - 32 q^{2} - 40 q^{3} - 24 q^{5} - 64 q^{6} - 32 q^{7} - 16 q^{8} - 32 q^{10} - 64 q^{11} - 88 q^{12} - 32 q^{13} - 32 q^{15} - 80 q^{16} - 56 q^{17} - 64 q^{18} - 64 q^{20} - 64 q^{21} - 32 q^{23} + 48 q^{24} + 160 q^{25} - 80 q^{26} - 64 q^{27} + 16 q^{28} + 40 q^{30} - 64 q^{31} - 80 q^{32} - 48 q^{33} - 32 q^{35} - 64 q^{36} - 120 q^{37} - 80 q^{38} - 96 q^{40} - 80 q^{41} + 56 q^{42} + 96 q^{43} + 128 q^{44} - 72 q^{45} + 80 q^{46} + 40 q^{47} - 8 q^{48} - 240 q^{49} - 32 q^{50} + 144 q^{51} + 40 q^{52} - 112 q^{53} + 224 q^{54} + 168 q^{55} - 24 q^{57} - 96 q^{58} + 144 q^{59} - 112 q^{60} - 96 q^{61} + 448 q^{62} - 24 q^{63} - 64 q^{64} - 32 q^{65} + 320 q^{66} - 8 q^{67} - 56 q^{68} - 16 q^{69} - 40 q^{70} + 32 q^{71} - 64 q^{72} - 32 q^{73} - 8 q^{74} - 32 q^{75} - 16 q^{76} - 24 q^{77} - 32 q^{78} - 80 q^{80} - 112 q^{81} + 192 q^{82} - 48 q^{84} + 48 q^{85} - 80 q^{86} - 168 q^{87} + 136 q^{88} - 80 q^{89} - 32 q^{90} - 240 q^{91} - 272 q^{92} + 72 q^{93} + 96 q^{94} - 144 q^{95} - 160 q^{96} - 8 q^{97} + 96 q^{98} - 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2005, [\chi])\) into newform subspaces

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