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Properties

Label 819.6.db
Level $819$
Weight $6$
Character orbit 819.db
Rep. character $\chi_{819}(209,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $960$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 819.db (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(819, [\chi])\).

Total New Old
Modular forms 1128 960 168
Cusp forms 1112 960 152
Eisenstein series 16 0 16

Trace form

\( 960 q + 7680 q^{4} - 760 q^{9} + O(q^{10}) \) \( 960 q + 7680 q^{4} - 760 q^{9} - 2790 q^{14} + 2172 q^{15} - 122880 q^{16} - 8020 q^{18} - 3902 q^{21} + 396 q^{23} - 300000 q^{25} + 71640 q^{29} - 24604 q^{30} + 14460 q^{32} - 104940 q^{36} - 105684 q^{42} + 75840 q^{46} - 3660 q^{49} - 153984 q^{50} - 1348 q^{51} - 228660 q^{56} + 240196 q^{57} - 20064 q^{58} + 404176 q^{60} + 137260 q^{63} - 3932160 q^{64} - 19872 q^{70} - 290776 q^{72} - 139986 q^{77} + 98020 q^{78} - 179016 q^{79} - 361712 q^{81} - 80226 q^{84} - 1740 q^{86} - 155316 q^{92} - 262748 q^{93} + 1938144 q^{95} - 634244 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(819, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(819, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(819, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)