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Properties

Label 1600.2.cq
Level $1600$
Weight $2$
Character orbit 1600.cq
Rep. character $\chi_{1600}(29,\cdot)$
Character field $\Q(\zeta_{80})$
Dimension $7616$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.cq (of order \(80\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1600 \)
Character field: \(\Q(\zeta_{80})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1600, [\chi])\).

Total New Old
Modular forms 7744 7744 0
Cusp forms 7616 7616 0
Eisenstein series 128 128 0

Trace form

\( 7616 q - 40 q^{2} - 40 q^{3} - 24 q^{4} - 32 q^{5} - 24 q^{6} - 40 q^{8} - 24 q^{9} + O(q^{10}) \) \( 7616 q - 40 q^{2} - 40 q^{3} - 24 q^{4} - 32 q^{5} - 24 q^{6} - 40 q^{8} - 24 q^{9} - 32 q^{10} - 24 q^{11} - 40 q^{12} - 40 q^{13} - 24 q^{14} - 32 q^{15} - 24 q^{16} - 40 q^{17} - 24 q^{19} - 32 q^{20} - 24 q^{21} - 40 q^{22} - 40 q^{23} - 64 q^{24} - 32 q^{25} + 16 q^{26} - 40 q^{27} - 40 q^{28} - 24 q^{29} - 112 q^{30} - 24 q^{34} - 32 q^{35} - 264 q^{36} - 40 q^{37} - 40 q^{38} - 24 q^{39} + 128 q^{40} - 24 q^{41} - 40 q^{42} - 24 q^{44} - 32 q^{45} - 24 q^{46} - 40 q^{47} - 40 q^{48} - 64 q^{49} - 56 q^{50} - 64 q^{51} - 40 q^{52} - 40 q^{53} - 24 q^{54} + 32 q^{55} - 24 q^{56} - 40 q^{58} - 24 q^{59} - 128 q^{60} - 24 q^{61} - 40 q^{62} - 80 q^{63} - 24 q^{64} - 64 q^{65} + 8 q^{66} - 40 q^{67} - 24 q^{69} - 128 q^{70} - 24 q^{71} - 40 q^{72} - 40 q^{73} - 64 q^{74} + 32 q^{75} - 64 q^{76} - 40 q^{77} - 40 q^{78} - 24 q^{79} - 56 q^{80} - 24 q^{81} - 40 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 40 q^{87} - 40 q^{88} - 24 q^{89} - 32 q^{90} - 24 q^{91} - 40 q^{92} + 56 q^{94} - 24 q^{96} - 40 q^{98} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1600, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.