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Properties

Label 847.6.b
Level $847$
Weight $6$
Character orbit 847.b
Rep. character $\chi_{847}(846,\cdot)$
Character field $\Q$
Dimension $352$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 847.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 452 368 84
Cusp forms 428 352 76
Eisenstein series 24 16 8

Trace form

\( 352 q - 5522 q^{4} - 27432 q^{9} + O(q^{10}) \) \( 352 q - 5522 q^{4} - 27432 q^{9} - 2006 q^{14} + 924 q^{15} + 88158 q^{16} - 6088 q^{23} - 206288 q^{25} + 477902 q^{36} - 31584 q^{37} - 40912 q^{42} - 23424 q^{49} + 141392 q^{53} + 45874 q^{56} - 163548 q^{58} - 42428 q^{60} - 1234494 q^{64} - 212964 q^{67} - 26680 q^{70} + 60156 q^{71} + 11932 q^{78} + 1851944 q^{81} - 251804 q^{86} + 485260 q^{91} - 20436 q^{92} + 984348 q^{93} + O(q^{100}) \)

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.

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

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