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Properties

Label 800.6.by
Level $800$
Weight $6$
Character orbit 800.by
Rep. character $\chi_{800}(29,\cdot)$
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.by (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

\( 9568 q - 20 q^{2} - 20 q^{3} - 12 q^{4} - 16 q^{5} - 12 q^{6} - 20 q^{8} - 12 q^{9} + O(q^{10}) \) \( 9568 q - 20 q^{2} - 20 q^{3} - 12 q^{4} - 16 q^{5} - 12 q^{6} - 20 q^{8} - 12 q^{9} - 16 q^{10} - 12 q^{11} - 20 q^{12} - 20 q^{13} - 12 q^{14} - 12 q^{16} - 12 q^{19} - 16 q^{20} - 12 q^{21} - 20 q^{22} - 20 q^{23} - 32 q^{24} - 16 q^{25} + 25928 q^{26} - 20 q^{27} - 20 q^{28} - 12 q^{29} + 32552 q^{30} + 46104 q^{31} - 40 q^{33} + 244 q^{34} + 4760 q^{35} - 93492 q^{36} - 20 q^{37} + 172040 q^{38} - 12 q^{39} + 64576 q^{40} - 12 q^{41} - 20 q^{42} - 12 q^{44} + 956 q^{45} - 12 q^{46} + 561840 q^{48} - 4536 q^{50} + 1912 q^{51} - 20 q^{52} - 20 q^{53} - 12 q^{54} + 110032 q^{55} - 12 q^{56} - 20 q^{58} - 12 q^{59} - 298032 q^{60} - 12 q^{61} - 20 q^{62} - 40 q^{63} + 414744 q^{64} - 32 q^{65} - 268 q^{66} - 20 q^{67} - 12 q^{69} + 343220 q^{70} - 12 q^{71} - 20 q^{72} - 20 q^{73} - 48520 q^{74} + 193232 q^{75} - 32 q^{76} - 20 q^{77} - 20 q^{78} - 493188 q^{80} - 20 q^{83} - 209924 q^{84} + 12484 q^{85} - 12 q^{86} - 20 q^{87} + 1557360 q^{88} - 12 q^{89} + 564620 q^{90} - 12 q^{91} + 1731400 q^{92} - 118572 q^{94} - 32 q^{95} + 595068 q^{96} - 40 q^{97} + 620 q^{98} - 1976 q^{99} + O(q^{100}) \)

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.