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Properties

Label 2005.2.m
Level $2005$
Weight $2$
Character orbit 2005.m
Rep. character $\chi_{2005}(356,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $536$
Sturm bound $402$

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Defining parameters

Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.m (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 401 \)
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 816 536 280
Cusp forms 800 536 264
Eisenstein series 16 0 16

Trace form

\( 536 q - 8 q^{5} + 8 q^{6} - 8 q^{9} + O(q^{10}) \) \( 536 q - 8 q^{5} + 8 q^{6} - 8 q^{9} - 64 q^{12} - 8 q^{13} - 16 q^{14} + 8 q^{15} - 648 q^{16} + 8 q^{17} + 24 q^{19} - 56 q^{21} - 32 q^{23} - 24 q^{24} + 536 q^{25} - 24 q^{26} + 40 q^{28} - 16 q^{31} + 8 q^{35} + 32 q^{37} + 32 q^{38} + 16 q^{39} - 32 q^{41} + 40 q^{42} - 16 q^{43} + 8 q^{44} - 24 q^{45} + 24 q^{46} + 64 q^{48} + 32 q^{51} + 64 q^{52} - 48 q^{54} - 16 q^{55} - 8 q^{58} - 32 q^{59} + 56 q^{60} + 8 q^{61} - 32 q^{62} - 144 q^{63} + 40 q^{65} + 40 q^{66} - 24 q^{67} + 56 q^{68} + 112 q^{70} - 8 q^{71} - 152 q^{72} - 72 q^{73} - 72 q^{74} - 40 q^{76} + 48 q^{79} + 56 q^{80} - 152 q^{82} + 144 q^{83} + 24 q^{84} - 48 q^{86} + 96 q^{87} - 48 q^{88} + 24 q^{89} + 72 q^{91} + 160 q^{92} + 160 q^{96} + 104 q^{97} - 264 q^{98} + O(q^{100}) \)

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

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