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Properties

Label 2005.2.be
Level $2005$
Weight $2$
Character orbit 2005.be
Rep. character $\chi_{2005}(114,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $3168$
Sturm bound $402$

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Defining parameters

Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.be (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2005 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(402\)

Dimensions

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

Total New Old
Modular forms 3232 3232 0
Cusp forms 3168 3168 0
Eisenstein series 64 64 0

Trace form

\( 3168 q - 40 q^{4} + 12 q^{5} - 32 q^{6} - 40 q^{9} + O(q^{10}) \) \( 3168 q - 40 q^{4} + 12 q^{5} - 32 q^{6} - 40 q^{9} - 40 q^{10} - 32 q^{11} + 8 q^{14} - 32 q^{15} + 720 q^{16} - 32 q^{19} - 64 q^{21} - 40 q^{24} - 84 q^{25} + 16 q^{26} - 256 q^{29} + 4 q^{30} - 32 q^{31} - 32 q^{34} - 36 q^{35} - 72 q^{36} + 256 q^{39} - 216 q^{40} - 16 q^{41} + 48 q^{44} - 8 q^{45} + 32 q^{46} - 160 q^{49} - 24 q^{50} + 104 q^{51} + 64 q^{54} - 20 q^{55} + 48 q^{59} - 236 q^{60} - 64 q^{61} - 40 q^{64} - 36 q^{65} - 320 q^{66} - 40 q^{69} + 28 q^{70} + 16 q^{71} + 48 q^{74} - 12 q^{75} + 24 q^{76} - 88 q^{79} + 92 q^{80} + 160 q^{81} - 104 q^{84} - 44 q^{85} - 200 q^{86} + 8 q^{89} + 140 q^{90} - 120 q^{91} - 360 q^{94} + 92 q^{95} - 16 q^{96} - 160 q^{99} + O(q^{100}) \)

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.