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Properties

Label 800.3.cb
Level $800$
Weight $3$
Character orbit 800.cb
Rep. character $\chi_{800}(11,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $3808$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 800.cb (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 800 \)
Character field: \(\Q(\zeta_{40})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(800, [\chi])\).

Total New Old
Modular forms 3872 3872 0
Cusp forms 3808 3808 0
Eisenstein series 64 64 0

Trace form

\( 3808 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 16 q^{5} - 12 q^{6} - 32 q^{7} - 12 q^{8} - 12 q^{9} + O(q^{10}) \) \( 3808 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 16 q^{5} - 12 q^{6} - 32 q^{7} - 12 q^{8} - 12 q^{9} - 16 q^{10} - 12 q^{11} + 84 q^{12} - 12 q^{13} - 12 q^{14} - 32 q^{15} - 12 q^{16} - 32 q^{18} - 12 q^{19} - 16 q^{20} - 12 q^{21} - 236 q^{22} - 12 q^{23} - 32 q^{24} - 16 q^{25} - 232 q^{26} - 12 q^{27} - 12 q^{28} - 12 q^{29} - 40 q^{30} - 32 q^{32} - 24 q^{33} - 44 q^{34} - 112 q^{35} - 612 q^{36} - 12 q^{37} - 768 q^{38} - 12 q^{39} - 512 q^{40} - 12 q^{41} - 12 q^{42} - 32 q^{43} - 12 q^{44} + 20 q^{45} - 12 q^{46} - 24 q^{47} + 144 q^{48} - 328 q^{50} - 104 q^{51} - 12 q^{52} - 12 q^{53} - 12 q^{54} - 272 q^{55} - 12 q^{56} - 32 q^{57} - 716 q^{58} - 12 q^{59} + 1360 q^{60} - 12 q^{61} - 44 q^{62} - 552 q^{64} - 32 q^{65} + 20 q^{66} - 12 q^{67} + 456 q^{68} - 12 q^{69} + 644 q^{70} - 12 q^{71} + 828 q^{72} - 12 q^{73} + 408 q^{74} + 368 q^{75} - 32 q^{76} - 12 q^{77} + 140 q^{78} - 24 q^{79} + 148 q^{80} - 1312 q^{82} - 12 q^{83} - 772 q^{84} - 116 q^{85} - 12 q^{86} + 884 q^{87} + 1176 q^{88} - 12 q^{89} - 532 q^{90} - 12 q^{91} + 936 q^{92} - 104 q^{93} - 860 q^{94} - 1812 q^{96} - 24 q^{97} - 420 q^{98} + 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(800, [\chi])\) into newform subspaces

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