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Properties

Label 847.6.p
Level $847$
Weight $6$
Character orbit 847.p
Rep. character $\chi_{847}(76,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $4380$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 847.p (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 847 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 4420 4420 0
Cusp forms 4380 4380 0
Eisenstein series 40 40 0

Trace form

\( 4380 q - 22 q^{2} + 6936 q^{4} - 11 q^{7} - 22 q^{8} - 351800 q^{9} + O(q^{10}) \) \( 4380 q - 22 q^{2} + 6936 q^{4} - 11 q^{7} - 22 q^{8} - 351800 q^{9} + 1468 q^{11} - 1745 q^{14} + 198 q^{15} - 107944 q^{16} + 4620 q^{18} + 2662 q^{21} + 12540 q^{22} - 1492 q^{23} + 262440 q^{25} - 11 q^{28} - 22 q^{29} + 5324 q^{30} - 22 q^{32} - 11 q^{35} - 545902 q^{36} + 576 q^{37} + 5324 q^{39} - 37268 q^{42} - 22 q^{43} - 42397 q^{44} - 22 q^{46} - 104003 q^{49} - 22 q^{50} - 267036 q^{51} - 94794 q^{53} - 45587 q^{56} + 5324 q^{57} + 116135 q^{58} - 66088 q^{60} - 416460 q^{63} + 2132980 q^{64} - 22 q^{65} + 68798 q^{67} + 67925 q^{70} - 83706 q^{71} - 715572 q^{72} - 22 q^{74} + 111815 q^{77} - 20724 q^{78} + 685938 q^{79} + 27707308 q^{81} + 2662 q^{84} - 204908 q^{85} - 523042 q^{86} + 608276 q^{88} + 41470 q^{91} - 1070002 q^{92} - 38390 q^{93} + 575586 q^{95} - 1055659 q^{98} - 2006256 q^{99} + O(q^{100}) \)

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.