Properties

Label 2005.2.r
Level $2005$
Weight $2$
Character orbit 2005.r
Rep. character $\chi_{2005}(39,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $800$
Sturm bound $402$

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Defining parameters

Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.r (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2005 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(402\)

Dimensions

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

Total New Old
Modular forms 816 816 0
Cusp forms 800 800 0
Eisenstein series 16 16 0

Trace form

\( 800 q + 194 q^{4} + 3 q^{5} - 20 q^{6} + 180 q^{9} + O(q^{10}) \) \( 800 q + 194 q^{4} + 3 q^{5} - 20 q^{6} + 180 q^{9} - 3 q^{10} - 16 q^{11} - 12 q^{14} - 5 q^{15} - 222 q^{16} - 12 q^{19} + 8 q^{20} - 8 q^{21} - 22 q^{24} - 19 q^{25} - 44 q^{26} - 64 q^{29} - 36 q^{30} - 18 q^{31} + 10 q^{34} - 18 q^{35} - 232 q^{36} + 4 q^{39} - 25 q^{40} - 40 q^{41} + 130 q^{44} + 74 q^{45} - 44 q^{46} + 188 q^{49} - q^{50} - 52 q^{51} + 34 q^{54} - 6 q^{55} + 160 q^{56} + 50 q^{59} - 75 q^{60} - 42 q^{61} + 250 q^{64} - 92 q^{65} - 94 q^{66} - 98 q^{69} + 67 q^{70} + 48 q^{71} - 21 q^{75} - 4 q^{76} - 22 q^{79} + 70 q^{80} - 234 q^{81} + 56 q^{84} + 38 q^{85} - 86 q^{86} + 6 q^{89} - 39 q^{90} - 84 q^{91} - 80 q^{94} + 34 q^{95} + 148 q^{96} + 56 q^{99} + O(q^{100}) \)

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

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