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Properties

Label 2005.2.w
Level $2005$
Weight $2$
Character orbit 2005.w
Rep. character $\chi_{2005}(164,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1600$
Sturm bound $402$

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Defining parameters

Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.w (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2005 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(402\)

Dimensions

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

Total New Old
Modular forms 1632 1632 0
Cusp forms 1600 1600 0
Eisenstein series 32 32 0

Trace form

\( 1600 q - 412 q^{4} - 12 q^{6} + O(q^{10}) \) \( 1600 q - 412 q^{4} - 12 q^{6} - 10 q^{10} - 20 q^{11} + 20 q^{14} - 12 q^{15} - 412 q^{16} + 28 q^{21} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 152 q^{29} + 40 q^{30} - 4 q^{31} - 32 q^{34} + 40 q^{36} - 128 q^{39} + 10 q^{40} - 88 q^{41} + 100 q^{44} + 72 q^{46} - 392 q^{49} - 10 q^{50} + 68 q^{51} + 4 q^{54} - 40 q^{55} - 224 q^{56} - 52 q^{59} + 138 q^{60} + 4 q^{61} - 508 q^{64} - 24 q^{65} + 116 q^{66} + 68 q^{69} - 18 q^{70} - 12 q^{71} - 80 q^{74} - 52 q^{75} - 36 q^{76} + 8 q^{79} + 208 q^{80} + 296 q^{81} - 16 q^{84} + 36 q^{85} - 12 q^{86} - 20 q^{89} - 174 q^{90} - 16 q^{91} - 148 q^{94} + 62 q^{95} - 200 q^{96} - 104 q^{99} + O(q^{100}) \)

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.