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Properties

Label 2005.2.bi
Level $2005$
Weight $2$
Character orbit 2005.bi
Rep. character $\chi_{2005}(224,\cdot)$
Character field $\Q(\zeta_{50})$
Dimension $4000$
Sturm bound $402$

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Defining parameters

Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.bi (of order \(50\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2005 \)
Character field: \(\Q(\zeta_{50})\)
Sturm bound: \(402\)

Dimensions

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

Total New Old
Modular forms 4080 4080 0
Cusp forms 4000 4000 0
Eisenstein series 80 80 0

Trace form

\( 4000 q - 40 q^{4} - 5 q^{5} - 30 q^{6} - 30 q^{9} + O(q^{10}) \) \( 4000 q - 40 q^{4} - 5 q^{5} - 30 q^{6} - 30 q^{9} - 20 q^{10} - 30 q^{11} - 50 q^{14} - 30 q^{15} - 40 q^{16} - 30 q^{19} - 40 q^{20} - 80 q^{21} - 40 q^{24} - 75 q^{25} + 10 q^{26} + 60 q^{29} - 40 q^{30} - 40 q^{31} - 40 q^{34} - 15 q^{35} - 10 q^{36} - 50 q^{39} + 40 q^{40} - 160 q^{41} - 180 q^{44} - 110 q^{45} - 10 q^{46} - 70 q^{49} - 40 q^{50} + 10 q^{51} - 120 q^{54} - 5 q^{55} - 150 q^{56} - 140 q^{59} + 255 q^{60} - 50 q^{61} - 120 q^{64} + 65 q^{65} - 330 q^{66} + 60 q^{69} + 90 q^{70} - 30 q^{71} + 240 q^{74} - 30 q^{76} - 40 q^{79} + 200 q^{80} - 40 q^{81} - 110 q^{84} - 10 q^{85} - 60 q^{86} + 290 q^{89} + 435 q^{90} - 30 q^{91} + 110 q^{94} + 165 q^{95} - 190 q^{96} + 50 q^{99} + O(q^{100}) \)

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.