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Properties

Label 200.6.v
Level $200$
Weight $6$
Character orbit 200.v
Rep. character $\chi_{200}(3,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1184$
Sturm bound $180$

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Defining parameters

Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 200.v (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(180\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(200, [\chi])\).

Total New Old
Modular forms 1216 1216 0
Cusp forms 1184 1184 0
Eisenstein series 32 32 0

Trace form

\( 1184 q - 8 q^{2} - 16 q^{3} - 10 q^{4} - 6 q^{6} - 254 q^{8} - 20 q^{9} + O(q^{10}) \) \( 1184 q - 8 q^{2} - 16 q^{3} - 10 q^{4} - 6 q^{6} - 254 q^{8} - 20 q^{9} + 560 q^{10} - 12 q^{11} + 298 q^{12} - 10 q^{14} - 6 q^{16} + 388 q^{17} - 3380 q^{18} - 20 q^{19} - 1370 q^{20} + 3138 q^{22} + 3100 q^{25} - 16 q^{26} - 988 q^{27} + 10010 q^{28} - 21110 q^{30} - 7978 q^{32} + 956 q^{33} - 10 q^{34} + 4760 q^{35} - 4102 q^{36} - 19216 q^{38} - 18980 q^{40} - 12 q^{41} + 158830 q^{42} - 1328 q^{43} - 51740 q^{44} - 6 q^{46} + 187144 q^{48} - 117590 q^{50} - 32 q^{51} + 191460 q^{52} + 66160 q^{54} - 6 q^{56} - 988 q^{57} + 205720 q^{58} - 20 q^{59} - 472090 q^{60} - 54800 q^{62} + 345620 q^{64} - 17700 q^{65} + 31098 q^{66} - 89272 q^{67} + 158154 q^{68} - 116990 q^{70} + 1240 q^{72} + 25164 q^{73} + 127720 q^{75} - 4112 q^{76} + 159000 q^{78} + 167350 q^{80} + 1732092 q^{81} + 742618 q^{82} + 126424 q^{83} + 78470 q^{84} - 6 q^{86} - 1247266 q^{88} + 877880 q^{89} - 999030 q^{90} - 12 q^{91} - 491930 q^{92} + 385750 q^{94} - 134106 q^{96} + 448284 q^{97} + 1238016 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(200, [\chi])\) into newform subspaces

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