Properties

Label 2005.2.n
Level $2005$
Weight $2$
Character orbit 2005.n
Rep. character $\chi_{2005}(499,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $792$
Sturm bound $402$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.n (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2005 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(402\)

Dimensions

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

Total New Old
Modular forms 808 808 0
Cusp forms 792 792 0
Eisenstein series 16 16 0

Trace form

\( 792 q + 8 q^{5} - 8 q^{6} + O(q^{10}) \) \( 792 q + 8 q^{5} - 8 q^{6} + 20 q^{10} - 8 q^{11} - 48 q^{14} + 12 q^{15} - 760 q^{16} - 8 q^{19} + 24 q^{21} - 56 q^{25} + 24 q^{26} - 64 q^{29} - 24 q^{30} - 8 q^{31} - 8 q^{34} + 16 q^{35} + 32 q^{36} + 64 q^{39} + 156 q^{40} + 96 q^{41} + 72 q^{44} - 12 q^{45} - 72 q^{46} + 4 q^{50} - 144 q^{51} - 144 q^{54} - 60 q^{55} - 88 q^{59} - 4 q^{60} + 64 q^{61} + 16 q^{65} - 80 q^{66} - 48 q^{70} - 16 q^{71} - 88 q^{74} + 92 q^{75} - 64 q^{76} + 48 q^{79} + 128 q^{80} + 64 q^{84} + 24 q^{85} + 160 q^{86} - 48 q^{89} - 80 q^{91} - 112 q^{95} - 24 q^{96} + O(q^{100}) \)

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

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