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Properties

Label 847.6.bc
Level $847$
Weight $6$
Character orbit 847.bc
Rep. character $\chi_{847}(4,\cdot)$
Character field $\Q(\zeta_{165})$
Dimension $35040$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 847.bc (of order \(165\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 847 \)
Character field: \(\Q(\zeta_{165})\)
Sturm bound: \(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(847, [\chi])\).

Total New Old
Modular forms 35360 35360 0
Cusp forms 35040 35040 0
Eisenstein series 320 320 0

Trace form

\( 35040 q - 43 q^{2} - 30 q^{3} - 7039 q^{4} - 63 q^{5} - 1028 q^{6} + 19 q^{7} - 584 q^{8} + 351180 q^{9} + O(q^{10}) \) \( 35040 q - 43 q^{2} - 30 q^{3} - 7039 q^{4} - 63 q^{5} - 1028 q^{6} + 19 q^{7} - 584 q^{8} + 351180 q^{9} - 3740 q^{10} - 1332 q^{11} - 4474 q^{12} - 1516 q^{13} + 510 q^{14} - 18750 q^{15} - 107551 q^{16} - 501 q^{17} + 1793 q^{18} + 4427 q^{19} + 6556 q^{20} - 9295 q^{21} - 276 q^{22} - 1180 q^{23} + 6980 q^{24} - 271277 q^{25} - 9257 q^{26} + 2238 q^{27} + 14314 q^{28} - 3576 q^{29} - 21511 q^{30} + 9925 q^{31} - 30700 q^{32} + 18432 q^{33} + 69152 q^{34} - 37053 q^{35} + 1073764 q^{36} + 14996 q^{37} - 89 q^{38} + 20236 q^{39} - 240200 q^{40} - 75586 q^{41} + 56445 q^{42} + 2204 q^{43} - 182101 q^{44} - 108725 q^{45} - 45090 q^{46} + 27459 q^{47} - 28476 q^{48} + 94881 q^{49} - 52614 q^{50} + 386731 q^{51} - 52187 q^{52} + 226691 q^{53} + 111044 q^{54} - 1948 q^{55} + 75480 q^{56} + 240018 q^{57} - 137913 q^{58} + 37909 q^{59} - 58138 q^{60} + 171256 q^{61} - 114048 q^{62} + 89637 q^{63} + 3872400 q^{64} + 3334 q^{65} - 273690 q^{66} - 68852 q^{67} - 133527 q^{68} - 83396 q^{69} + 6961 q^{70} + 479084 q^{71} + 394068 q^{72} + 109276 q^{73} - 307949 q^{74} + 157349 q^{75} + 1898320 q^{76} + 442058 q^{77} - 122654 q^{78} + 93374 q^{79} + 387913 q^{80} + 27771912 q^{81} - 165633 q^{82} - 281268 q^{83} - 577438 q^{84} - 76566 q^{85} - 579502 q^{86} - 1252525 q^{87} - 316163 q^{88} - 428409 q^{89} - 1200258 q^{90} + 77571 q^{91} + 1092346 q^{92} + 839747 q^{93} - 830594 q^{94} - 703734 q^{95} - 104051 q^{96} + 1296230 q^{97} + 1758484 q^{98} - 2718078 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(847, [\chi])\) into newform subspaces

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