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Properties

Label 2005.2.bc
Level $2005$
Weight $2$
Character orbit 2005.bc
Rep. character $\chi_{2005}(51,\cdot)$
Character field $\Q(\zeta_{25})$
Dimension $2680$
Sturm bound $402$

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Defining parameters

Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.bc (of order \(25\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 401 \)
Character field: \(\Q(\zeta_{25})\)
Sturm bound: \(402\)

Dimensions

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

Total New Old
Modular forms 4040 2680 1360
Cusp forms 3960 2680 1280
Eisenstein series 80 0 80

Trace form

\( 2680 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{6} - 10 q^{8} - 30 q^{9} + O(q^{10}) \) \( 2680 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{6} - 10 q^{8} - 30 q^{9} + 60 q^{11} - 10 q^{13} - 10 q^{14} - 50 q^{16} + 40 q^{18} - 40 q^{19} + 120 q^{20} + 160 q^{21} + 50 q^{22} - 30 q^{24} - 40 q^{26} - 40 q^{27} - 140 q^{32} - 30 q^{34} - 40 q^{35} - 30 q^{36} - 40 q^{37} + 30 q^{38} - 100 q^{39} + 120 q^{41} - 50 q^{42} - 50 q^{43} - 150 q^{44} + 120 q^{45} - 80 q^{46} - 360 q^{48} - 30 q^{49} - 150 q^{51} + 280 q^{52} - 10 q^{53} - 110 q^{54} - 140 q^{56} - 30 q^{57} - 20 q^{58} - 50 q^{59} - 30 q^{61} - 70 q^{62} + 330 q^{63} - 110 q^{64} + 120 q^{66} - 30 q^{67} - 120 q^{68} - 90 q^{70} - 50 q^{71} - 290 q^{72} + 40 q^{74} - 300 q^{76} + 120 q^{77} - 130 q^{78} - 40 q^{79} + 180 q^{81} + 340 q^{82} - 140 q^{83} + 340 q^{84} - 30 q^{85} + 230 q^{86} - 250 q^{88} + 220 q^{89} - 10 q^{91} + 510 q^{92} + 80 q^{93} + 100 q^{94} + 450 q^{96} - 120 q^{97} + 140 q^{98} - 150 q^{99} + O(q^{100}) \)

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

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