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Properties

Label 2005.2.e
Level $2005$
Weight $2$
Character orbit 2005.e
Rep. character $\chi_{2005}(381,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $268$
Sturm bound $402$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 404 268 136
Cusp forms 396 268 128
Eisenstein series 8 0 8

Trace form

\( 268 q - 4 q^{3} - 276 q^{4} + 4 q^{5} + O(q^{10}) \) \( 268 q - 4 q^{3} - 276 q^{4} + 4 q^{5} + 32 q^{12} + 4 q^{13} + 8 q^{14} + 4 q^{15} + 308 q^{16} - 8 q^{17} - 92 q^{18} + 8 q^{19} - 12 q^{20} + 24 q^{21} - 8 q^{22} + 16 q^{23} - 20 q^{24} + 268 q^{25} + 20 q^{27} - 8 q^{29} - 4 q^{30} + 4 q^{31} - 4 q^{33} - 20 q^{34} + 16 q^{37} + 16 q^{38} + 8 q^{39} + 24 q^{41} + 20 q^{42} + 28 q^{46} - 36 q^{48} - 220 q^{49} - 64 q^{51} + 16 q^{52} + 28 q^{53} + 48 q^{54} - 120 q^{56} - 104 q^{57} + 12 q^{59} + 12 q^{60} - 16 q^{61} + 4 q^{62} + 72 q^{63} - 356 q^{64} + 20 q^{65} - 120 q^{66} - 40 q^{67} - 132 q^{68} + 8 q^{69} + 40 q^{70} + 60 q^{71} + 236 q^{72} - 80 q^{74} - 4 q^{75} - 84 q^{76} + 40 q^{77} - 68 q^{79} + 28 q^{80} - 116 q^{81} - 40 q^{83} - 160 q^{84} - 12 q^{85} + 16 q^{87} + 24 q^{88} - 20 q^{90} - 4 q^{91} - 60 q^{92} + 24 q^{93} + 40 q^{94} - 8 q^{95} - 12 q^{96} - 4 q^{97} - 176 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(2005, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2005, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(401, [\chi])\)\(^{\oplus 2}\)