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Properties

Label 2005.2.bu
Level $2005$
Weight $2$
Character orbit 2005.bu
Rep. character $\chi_{2005}(9,\cdot)$
Character field $\Q(\zeta_{200})$
Dimension $15840$
Sturm bound $402$

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Defining parameters

Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.bu (of order \(200\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2005 \)
Character field: \(\Q(\zeta_{200})\)
Sturm bound: \(402\)

Dimensions

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

Total New Old
Modular forms 16160 16160 0
Cusp forms 15840 15840 0
Eisenstein series 320 320 0

Trace form

\( 15840 q - 160 q^{4} - 120 q^{5} - 160 q^{6} - 160 q^{9} + O(q^{10}) \) \( 15840 q - 160 q^{4} - 120 q^{5} - 160 q^{6} - 160 q^{9} - 80 q^{10} - 160 q^{11} - 160 q^{14} - 80 q^{15} - 160 q^{16} - 160 q^{19} - 160 q^{21} - 160 q^{24} + 40 q^{25} - 240 q^{26} + 120 q^{29} - 80 q^{30} - 160 q^{31} - 160 q^{34} - 80 q^{35} - 160 q^{36} - 520 q^{39} - 240 q^{40} + 320 q^{41} - 320 q^{44} - 80 q^{45} - 160 q^{46} - 40 q^{49} - 80 q^{50} - 160 q^{51} - 120 q^{54} - 20 q^{55} - 200 q^{56} - 160 q^{59} - 160 q^{60} - 160 q^{64} - 80 q^{65} + 200 q^{66} - 160 q^{69} - 80 q^{70} - 200 q^{71} - 160 q^{74} - 180 q^{75} - 160 q^{76} - 160 q^{79} + 80 q^{80} - 360 q^{81} - 160 q^{84} - 80 q^{85} - 160 q^{86} - 160 q^{89} - 240 q^{90} + 160 q^{94} - 80 q^{95} - 160 q^{96} - 40 q^{99} + O(q^{100}) \)

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.