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Properties

Label 819.6.n
Level $819$
Weight $6$
Character orbit 819.n
Rep. character $\chi_{819}(100,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $462$
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.n (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
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 1136 470 666
Cusp forms 1104 462 642
Eisenstein series 32 8 24

Trace form

\( 462 q - q^{2} - 3647 q^{4} + 2 q^{5} + 170 q^{7} + 72 q^{8} + O(q^{10}) \) \( 462 q - q^{2} - 3647 q^{4} + 2 q^{5} + 170 q^{7} + 72 q^{8} - 674 q^{10} - 778 q^{11} - 588 q^{13} + 1804 q^{14} - 57179 q^{16} - 1771 q^{17} - 1396 q^{19} - 2858 q^{20} - 1388 q^{22} - 1715 q^{23} - 138065 q^{25} - 11922 q^{26} + 6434 q^{28} + 556 q^{29} + 8979 q^{31} + 6357 q^{32} + 25792 q^{34} + 6607 q^{35} + 6683 q^{37} + 5050 q^{38} - 3878 q^{40} - 16765 q^{41} - 2612 q^{43} + 29238 q^{44} - 16550 q^{46} + 23222 q^{47} - 27732 q^{49} + 9220 q^{50} - 148264 q^{52} - 5929 q^{53} + 38286 q^{55} + 51519 q^{56} - 160938 q^{58} + 64879 q^{59} - 275864 q^{61} + 18796 q^{62} + 1739400 q^{64} - 87688 q^{65} - 99492 q^{67} - 76179 q^{68} + 126570 q^{70} + 60625 q^{71} + 130845 q^{73} + 166385 q^{74} + 3454 q^{76} - 11678 q^{77} - 22188 q^{79} + 46648 q^{80} + 45328 q^{82} - 71466 q^{83} + 5249 q^{85} - 307044 q^{86} + 214566 q^{88} + 110204 q^{89} - 165011 q^{91} - 91038 q^{92} - 345508 q^{94} + 207615 q^{95} - 188008 q^{97} + 311297 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{6}^{\mathrm{old}}(819, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(819, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)