↑

Properties

Label 819.6.k
Level $819$
Weight $6$
Character orbit 819.k
Rep. character $\chi_{819}(529,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $1112$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 819.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 819 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(819, [\chi])\).

Total New Old
Modular forms 1128 1128 0
Cusp forms 1112 1112 0
Eisenstein series 16 16 0

Trace form

\( 1112 q - q^{2} + q^{3} - 8833 q^{4} + 2 q^{5} - 66 q^{6} - 118 q^{7} + 48 q^{8} - 109 q^{9} + O(q^{10}) \) \( 1112 q - q^{2} + q^{3} - 8833 q^{4} + 2 q^{5} - 66 q^{6} - 118 q^{7} + 48 q^{8} - 109 q^{9} + 66 q^{10} - 758 q^{11} + 1002 q^{12} + 179 q^{13} + 126 q^{14} - 371 q^{15} - 139297 q^{16} - 9252 q^{17} + 270 q^{18} + 64 q^{19} - 4228 q^{20} - 2735 q^{21} - 126 q^{22} - 2637 q^{23} + 4276 q^{24} - 337498 q^{25} + 6718 q^{26} - 2534 q^{27} + 7838 q^{28} - 1418 q^{29} - 182 q^{30} + 2164 q^{31} - 769 q^{32} - 16457 q^{33} - 36 q^{34} + 3107 q^{35} + 76 q^{36} - 5162 q^{37} + 39712 q^{38} - 229 q^{39} + 8364 q^{40} - 4 q^{41} - 48894 q^{42} + 18484 q^{43} + 26332 q^{44} + 15638 q^{45} + 252 q^{46} - 18856 q^{47} + 75888 q^{48} - 24478 q^{49} - 6970 q^{50} - 61176 q^{51} + 15617 q^{52} - 37690 q^{53} + 40302 q^{54} - 3129 q^{55} - 113948 q^{56} - 31466 q^{57} + 258 q^{58} - q^{59} + 9292 q^{60} + 24772 q^{61} + 109748 q^{62} + 120953 q^{63} + 4327472 q^{64} + 26393 q^{65} + 14267 q^{66} + 622 q^{67} + 217919 q^{68} + 49835 q^{69} - 21084 q^{70} - 28516 q^{71} + 248317 q^{72} + 42010 q^{73} + 84233 q^{74} - 73949 q^{75} - 12164 q^{76} - 78156 q^{77} + 42674 q^{78} - 114602 q^{79} - 8199 q^{80} + 157355 q^{81} + 66 q^{82} - 94070 q^{83} - 348600 q^{84} + 5727 q^{85} - 97492 q^{86} + 83524 q^{87} + 73602 q^{88} - 15294 q^{89} - 12168 q^{90} - 119020 q^{91} + 50642 q^{92} + 75954 q^{93} - 129 q^{94} - 47055 q^{95} - 232302 q^{96} - 69362 q^{97} - 1119662 q^{98} + 196221 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(819, [\chi])\) into newform subspaces

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