Properties

Label 847.6.l
Level $847$
Weight $6$
Character orbit 847.l
Rep. character $\chi_{847}(118,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1408$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 847.l (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 1808 1472 336
Cusp forms 1712 1408 304
Eisenstein series 96 64 32

Trace form

\( 1408 q + 10 q^{2} + 5532 q^{4} - 290 q^{7} + 170 q^{8} + 26892 q^{9} + O(q^{10}) \) \( 1408 q + 10 q^{2} + 5532 q^{4} - 290 q^{7} + 170 q^{8} + 26892 q^{9} - 189 q^{14} + 3816 q^{15} - 86388 q^{16} - 2015 q^{18} + 6008 q^{23} + 199918 q^{25} + 9125 q^{28} + 12630 q^{29} + 2440 q^{30} + 18960 q^{35} - 480322 q^{36} + 4974 q^{37} + 3810 q^{39} + 10892 q^{42} - 33095 q^{46} + 55054 q^{49} + 31260 q^{50} - 175990 q^{51} - 105522 q^{53} + 411386 q^{56} - 287910 q^{57} + 170873 q^{58} + 127448 q^{60} - 238580 q^{63} + 1646464 q^{64} - 588516 q^{67} + 220060 q^{70} - 320296 q^{71} - 19895 q^{72} + 1016470 q^{74} + 177988 q^{78} + 367230 q^{79} - 1960064 q^{81} - 95570 q^{84} - 145180 q^{85} - 788171 q^{86} - 520950 q^{91} - 45489 q^{92} - 632228 q^{93} + 626260 q^{95} + O(q^{100}) \)

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

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

Decomposition of \(S_{6}^{\mathrm{old}}(847, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(847, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)