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Properties

Label 819.6.eg
Level $819$
Weight $6$
Character orbit 819.eg
Rep. character $\chi_{819}(38,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1112$
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.eg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 819 \)
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 1128 0
Cusp forms 1112 1112 0
Eisenstein series 16 16 0

Trace form

\( 1112 q - 6 q^{3} + 17660 q^{4} - 222 q^{9} + O(q^{10}) \) \( 1112 q - 6 q^{3} + 17660 q^{4} - 222 q^{9} - 12 q^{10} - 198 q^{12} - 543 q^{13} - 6 q^{14} + 278396 q^{16} - 132 q^{22} - 15822 q^{23} + 337502 q^{25} - 10128 q^{26} - 7578 q^{27} - 12 q^{29} - 5722 q^{30} - 29580 q^{35} + 7580 q^{36} - 14976 q^{38} + 12369 q^{39} - 19140 q^{40} + 56316 q^{42} - 18492 q^{43} - 7794 q^{48} + 12236 q^{49} + 111178 q^{51} - 40899 q^{52} + 15576 q^{53} - 101040 q^{56} - 79728 q^{62} + 4321136 q^{64} + 219594 q^{66} - 6 q^{68} + 7404 q^{69} - 506562 q^{74} + 244788 q^{75} - 172902 q^{77} - 99575 q^{78} - 229200 q^{79} + 107658 q^{81} - 204 q^{82} + 409482 q^{87} + 61314 q^{88} + 113070 q^{90} + 88671 q^{91} - 849702 q^{92} + O(q^{100}) \)

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.