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Properties

Label 800.6.cd
Level $800$
Weight $6$
Character orbit 800.cd
Rep. character $\chi_{800}(3,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $9568$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 800.cd (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 800 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(800, [\chi])\).

Total New Old
Modular forms 9632 9632 0
Cusp forms 9568 9568 0
Eisenstein series 64 64 0

Trace form

\( 9568 q - 16 q^{2} - 16 q^{3} - 20 q^{4} - 16 q^{5} - 12 q^{6} - 32 q^{7} + 1952 q^{8} - 20 q^{9} + O(q^{10}) \) \( 9568 q - 16 q^{2} - 16 q^{3} - 20 q^{4} - 16 q^{5} - 12 q^{6} - 32 q^{7} + 1952 q^{8} - 20 q^{9} + 1052 q^{10} - 12 q^{11} - 1600 q^{12} - 16 q^{13} - 404 q^{14} - 32 q^{15} - 12 q^{16} + 112 q^{18} - 20 q^{19} - 1668 q^{20} - 4872 q^{21} - 5600 q^{22} - 12 q^{23} - 16 q^{25} - 32 q^{26} - 988 q^{27} - 16400 q^{28} - 20 q^{29} - 1404 q^{30} + 25564 q^{32} - 32 q^{33} - 20 q^{34} - 54792 q^{35} - 12 q^{36} - 16 q^{37} - 71696 q^{38} - 20 q^{39} - 124736 q^{40} - 12 q^{41} - 95992 q^{42} - 1328 q^{43} - 20 q^{44} - 16 q^{45} - 12 q^{46} - 32 q^{47} - 539072 q^{48} + 22511776 q^{49} - 144 q^{50} - 32 q^{51} - 128148 q^{52} - 16 q^{53} - 20 q^{54} + 110032 q^{55} - 336152 q^{56} - 97584 q^{58} - 20 q^{59} - 4112 q^{60} - 12 q^{61} - 103428 q^{62} - 537824 q^{63} - 691280 q^{64} - 32 q^{65} - 9312 q^{66} + 357008 q^{67} + 155812 q^{68} + 1924 q^{69} - 69164 q^{70} - 12 q^{71} + 48852 q^{72} - 20 q^{73} + 956 q^{75} - 32 q^{76} - 268928 q^{77} - 141732 q^{78} - 40 q^{79} - 116260 q^{80} + 68032 q^{82} - 126456 q^{83} - 201704 q^{84} - 16 q^{85} - 12 q^{86} - 20 q^{87} + 790244 q^{88} - 20 q^{89} + 528504 q^{90} - 336152 q^{91} - 110272 q^{92} - 988 q^{93} - 20 q^{94} - 12 q^{96} - 32 q^{97} - 176456 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

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