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Properties

Label 819.6.m
Level $819$
Weight $6$
Character orbit 819.m
Rep. character $\chi_{819}(274,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $720$
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.m (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
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 720 408
Cusp forms 1112 720 392
Eisenstein series 16 0 16

Trace form

\( 720 q + 16 q^{2} - 40 q^{3} - 5760 q^{4} + 116 q^{5} + 16 q^{6} - 1536 q^{8} - 8 q^{9} + O(q^{10}) \) \( 720 q + 16 q^{2} - 40 q^{3} - 5760 q^{4} + 116 q^{5} + 16 q^{6} - 1536 q^{8} - 8 q^{9} + 1020 q^{11} + 4480 q^{12} - 7192 q^{15} - 92160 q^{16} - 6024 q^{17} - 22888 q^{18} + 3576 q^{19} + 9076 q^{20} + 3792 q^{22} + 12008 q^{23} - 16004 q^{24} - 231612 q^{25} - 9544 q^{27} - 14832 q^{30} + 8868 q^{31} + 23852 q^{32} - 55444 q^{33} + 40632 q^{34} - 36380 q^{36} - 40056 q^{37} - 91880 q^{38} - 18600 q^{40} + 40628 q^{41} + 80360 q^{42} + 12612 q^{43} - 66944 q^{44} + 91124 q^{45} + 107760 q^{46} - 42256 q^{47} - 112740 q^{48} - 864360 q^{49} - 53560 q^{50} - 48572 q^{51} - 106176 q^{53} + 16240 q^{54} - 55176 q^{55} - 296988 q^{57} - 12464 q^{59} + 350384 q^{60} + 270120 q^{62} - 23128 q^{63} + 3164880 q^{64} + 67600 q^{65} + 12216 q^{66} - 31080 q^{67} + 112448 q^{68} - 119180 q^{69} - 255560 q^{71} + 192784 q^{72} + 321768 q^{73} - 152708 q^{74} - 159512 q^{75} - 186504 q^{76} + 855312 q^{80} - 244304 q^{81} + 222816 q^{82} + 173848 q^{83} + 548980 q^{86} - 778760 q^{87} + 361560 q^{88} - 695072 q^{89} - 2100908 q^{90} + 307876 q^{92} + 1013580 q^{93} + 57864 q^{94} - 107096 q^{95} - 393332 q^{96} + 242904 q^{97} - 76832 q^{98} - 427228 q^{99} + O(q^{100}) \)

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.

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

\( S_{6}^{\mathrm{old}}(819, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)