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Properties

Label 819.6.p
Level $819$
Weight $6$
Character orbit 819.p
Rep. character $\chi_{819}(16,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $1112$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 819.p (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

\( 1112 q - q^{2} + q^{3} - 8833 q^{4} - 4 q^{5} + 126 q^{6} + 59 q^{7} + 48 q^{8} - 109 q^{9} + O(q^{10}) \) \( 1112 q - q^{2} + q^{3} - 8833 q^{4} - 4 q^{5} + 126 q^{6} + 59 q^{7} + 48 q^{8} - 109 q^{9} + 66 q^{10} + 379 q^{11} - 552 q^{12} + 179 q^{13} - 66 q^{14} + 550 q^{15} - 139297 q^{16} - 9252 q^{17} - 1842 q^{18} + 64 q^{19} + 2114 q^{20} - 2006 q^{21} + 252 q^{22} - 2637 q^{23} - 1676 q^{24} + 674996 q^{25} + 6718 q^{26} - 2534 q^{27} + 7838 q^{28} + 2836 q^{29} - 581 q^{30} - 1082 q^{31} - 769 q^{32} + 30001 q^{33} - 36 q^{34} + 3107 q^{35} - 14804 q^{36} - 5162 q^{37} - 79424 q^{38} - 229 q^{39} - 16728 q^{40} + 2 q^{41} + 60360 q^{42} - 9242 q^{43} + 26332 q^{44} + 15638 q^{45} + 252 q^{46} + 9428 q^{47} - 60450 q^{48} + 12239 q^{49} + 3485 q^{50} - 1974 q^{51} + 9470 q^{52} - 37690 q^{53} + 40302 q^{54} - 3129 q^{55} - 57380 q^{56} - 31466 q^{57} - 129 q^{58} - q^{59} - 66071 q^{60} - 49544 q^{61} + 109748 q^{62} + 97607 q^{63} + 4327472 q^{64} + 19925 q^{65} - 112156 q^{66} - 1244 q^{67} + 217919 q^{68} + 43946 q^{69} - 8259 q^{70} - 28516 q^{71} + 182845 q^{72} + 42010 q^{73} + 84233 q^{74} - 73949 q^{75} + 6082 q^{76} + 117030 q^{77} - 3886 q^{78} + 57301 q^{79} - 8199 q^{80} - 58273 q^{81} + 66 q^{82} - 94070 q^{83} + 356886 q^{84} - 11454 q^{85} + 194984 q^{86} + 83524 q^{87} - 36801 q^{88} - 15294 q^{89} - 12168 q^{90} - 119020 q^{91} + 50642 q^{92} + 75954 q^{93} + 258 q^{94} - 47055 q^{95} - 263328 q^{96} + 34681 q^{97} - 1119662 q^{98} + 196221 q^{99} + O(q^{100}) \)

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.