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Properties

Label 819.6.bk
Level $819$
Weight $6$
Character orbit 819.bk
Rep. character $\chi_{819}(25,\cdot)$
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.bk (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

\( 1112 q - 2 q^{3} - 17668 q^{4} - 222 q^{9} + O(q^{10}) \) \( 1112 q - 2 q^{3} - 17668 q^{4} - 222 q^{9} + 124 q^{10} - 1882 q^{12} - 183 q^{13} + 254 q^{14} + 278652 q^{16} + 4620 q^{17} + 124 q^{22} - 5270 q^{23} + 337502 q^{25} + 3310 q^{26} - 2534 q^{27} + 2836 q^{29} - 19282 q^{30} - 12476 q^{35} - 11692 q^{36} + 29796 q^{38} - 1063 q^{39} - 10216 q^{40} - 27732 q^{42} + 18484 q^{43} + 12710 q^{48} + 12236 q^{49} - 44462 q^{51} + 9601 q^{52} - 64992 q^{53} + 12484 q^{55} + 103704 q^{56} - 99096 q^{61} - 272352 q^{62} - 4329360 q^{64} - 56140 q^{65} + 104802 q^{66} - 225918 q^{68} - 193000 q^{69} - 30450 q^{74} - 97168 q^{75} - 9598 q^{77} - 187705 q^{78} + 59040 q^{79} + 144906 q^{81} - 68 q^{82} - 155846 q^{87} - 69502 q^{88} + 133294 q^{90} + 52875 q^{91} + 629318 q^{92} + 508 q^{94} - 478188 q^{95} + O(q^{100}) \)

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.