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Properties

Label 847.6.ba
Level $847$
Weight $6$
Character orbit 847.ba
Rep. character $\chi_{847}(6,\cdot)$
Character field $\Q(\zeta_{110})$
Dimension $17520$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 847.ba (of order \(110\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 847 \)
Character field: \(\Q(\zeta_{110})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 17680 17680 0
Cusp forms 17520 17520 0
Eisenstein series 160 160 0

Trace form

\( 17520 q - 78 q^{2} - 7036 q^{4} - 334 q^{7} + 82 q^{8} + 351150 q^{9} + O(q^{10}) \) \( 17520 q - 78 q^{2} - 7036 q^{4} - 334 q^{7} + 82 q^{8} + 351150 q^{9} - 1568 q^{11} - 505 q^{14} + 4432 q^{15} + 109604 q^{16} - 6745 q^{18} - 2717 q^{21} - 37780 q^{22} + 1402 q^{23} - 268920 q^{25} + 9081 q^{28} + 12542 q^{29} - 2994 q^{30} - 88 q^{32} + 18916 q^{35} + 543372 q^{36} - 27296 q^{37} - 1624 q^{39} + 7193 q^{42} - 88 q^{43} + 156032 q^{44} - 33183 q^{46} + 135578 q^{49} + 31172 q^{50} + 90936 q^{51} + 130554 q^{53} + 45542 q^{56} - 293344 q^{57} - 108920 q^{58} + 150998 q^{60} + 177825 q^{63} - 1721120 q^{64} - 88 q^{65} - 68888 q^{67} + 125400 q^{70} - 176544 q^{71} + 695567 q^{72} + 1016382 q^{74} + 22450 q^{77} + 20634 q^{78} - 318818 q^{79} - 27815538 q^{81} - 98287 q^{84} + 59618 q^{85} - 517043 q^{86} - 1613336 q^{88} - 77215 q^{91} + 1003967 q^{92} + 390400 q^{93} + 50564 q^{95} + 1055604 q^{98} + 1857306 q^{99} + O(q^{100}) \)

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.