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Properties

Label 2005.2.u
Level $2005$
Weight $2$
Character orbit 2005.u
Rep. character $\chi_{2005}(147,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1592$
Sturm bound $402$

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Defining parameters

Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.u (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2005 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(402\)

Dimensions

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

Total New Old
Modular forms 1624 1624 0
Cusp forms 1592 1592 0
Eisenstein series 32 32 0

Trace form

\( 1592 q - 8 q^{2} - 16 q^{3} - 16 q^{5} - 16 q^{6} - 8 q^{7} + 8 q^{8} + O(q^{10}) \) \( 1592 q - 8 q^{2} - 16 q^{3} - 16 q^{5} - 16 q^{6} - 8 q^{7} + 8 q^{8} - 8 q^{10} - 16 q^{11} - 8 q^{13} - 8 q^{15} - 40 q^{17} + 24 q^{20} - 16 q^{21} + 48 q^{22} - 8 q^{23} + 48 q^{24} + 40 q^{25} - 40 q^{27} + 8 q^{28} - 16 q^{30} - 16 q^{31} - 24 q^{32} - 72 q^{33} - 8 q^{35} - 16 q^{36} - 40 q^{37} - 56 q^{38} + 8 q^{40} + 32 q^{42} - 56 q^{43} - 32 q^{44} + 32 q^{45} - 160 q^{46} + 64 q^{47} + 32 q^{48} - 8 q^{50} - 224 q^{51} - 24 q^{52} + 72 q^{53} + 144 q^{54} + 40 q^{55} - 80 q^{56} - 24 q^{58} + 144 q^{59} - 16 q^{60} + 16 q^{61} - 128 q^{62} - 16 q^{63} - 64 q^{64} - 8 q^{65} + 80 q^{66} - 32 q^{67} - 32 q^{68} - 16 q^{69} - 112 q^{71} - 16 q^{72} - 8 q^{73} - 8 q^{74} - 8 q^{75} - 64 q^{76} - 16 q^{77} + 72 q^{78} + 120 q^{80} + 32 q^{81} - 104 q^{82} - 48 q^{84} - 64 q^{85} + 8 q^{87} - 16 q^{88} - 80 q^{89} - 272 q^{90} - 160 q^{91} - 56 q^{92} + 96 q^{94} + 120 q^{95} + 80 q^{96} - 32 q^{97} - 168 q^{98} + 144 q^{99} + O(q^{100}) \)

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.