Properties

Label 2005.2.q
Level $2005$
Weight $2$
Character orbit 2005.q
Rep. character $\chi_{2005}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $800$
Sturm bound $402$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.q (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

\( 800 q + 194 q^{4} - 3 q^{5} - 220 q^{9} + O(q^{10}) \) \( 800 q + 194 q^{4} - 3 q^{5} - 220 q^{9} + 5 q^{10} + 4 q^{11} - 15 q^{15} - 190 q^{16} - 20 q^{19} - 8 q^{20} - 20 q^{21} - 10 q^{24} - 11 q^{25} - 40 q^{29} - 10 q^{31} - 10 q^{34} - 18 q^{35} + 200 q^{36} - 132 q^{39} - 25 q^{40} - 32 q^{41} + 10 q^{44} - 58 q^{45} + 20 q^{46} + 204 q^{49} - 13 q^{50} + 24 q^{51} - 70 q^{54} - 38 q^{55} + 64 q^{56} - 110 q^{59} - 155 q^{60} - 50 q^{61} + 234 q^{64} + 80 q^{65} - 150 q^{66} - 10 q^{69} - 21 q^{70} - 20 q^{71} + 40 q^{74} - 35 q^{75} - 10 q^{79} + 58 q^{80} - 270 q^{81} - 70 q^{85} + 90 q^{86} - 58 q^{89} - 39 q^{90} - 20 q^{91} - 84 q^{94} - 100 q^{95} + 100 q^{96} + O(q^{100}) \)

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

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