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Properties

Label 819.6.gi
Level $819$
Weight $6$
Character orbit 819.gi
Rep. character $\chi_{819}(115,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2224$
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.gi (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 819 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2256 2256 0
Cusp forms 2224 2224 0
Eisenstein series 32 32 0

Trace form

\( 2224 q - 4 q^{2} - 6 q^{4} - 6 q^{5} + 56 q^{7} - 80 q^{8} - 4 q^{9} + O(q^{10}) \) \( 2224 q - 4 q^{2} - 6 q^{4} - 6 q^{5} + 56 q^{7} - 80 q^{8} - 4 q^{9} - 24 q^{10} - 378 q^{11} - 4 q^{14} + 3166 q^{15} + 278526 q^{16} - 12 q^{17} - 5410 q^{18} - 12 q^{19} - 192 q^{20} + 1998 q^{21} - 8 q^{22} - 4692 q^{24} - 12 q^{26} + 15156 q^{27} - 5448 q^{28} - 5688 q^{29} + 18336 q^{30} - 6504 q^{31} - 1796 q^{32} - 29736 q^{33} - 22332 q^{35} - 42252 q^{36} - 10320 q^{37} - 5446 q^{39} - 12 q^{40} - 37096 q^{42} + 55452 q^{43} - 20164 q^{44} - 6 q^{45} + 124 q^{46} + 56556 q^{47} + 6144 q^{48} - 6 q^{49} + 712 q^{50} + 2916 q^{51} - 12294 q^{52} - 5200 q^{53} - 198 q^{54} - 12294 q^{56} + 124366 q^{57} - 126 q^{58} - 94600 q^{60} + 6 q^{61} - 13948 q^{63} + 35710 q^{65} + 296190 q^{66} + 1242 q^{67} - 17724 q^{69} - 46180 q^{70} + 35712 q^{71} - 409274 q^{72} - 12 q^{73} - 199300 q^{74} - 6 q^{75} - 5760 q^{76} - 78552 q^{77} + 316544 q^{78} + 144112 q^{79} - 885822 q^{80} - 223484 q^{81} - 24 q^{82} - 564396 q^{83} - 130142 q^{84} - 11454 q^{85} - 204906 q^{86} - 2922 q^{87} + 6 q^{88} - 12 q^{89} - 708588 q^{90} + 31424 q^{91} + 309172 q^{92} - 158208 q^{93} + 6 q^{94} - 1039734 q^{95} + 243258 q^{96} - 208074 q^{97} - 1279840 q^{98} - 8726 q^{99} + O(q^{100}) \)

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.