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Properties

Label 819.6.y
Level $819$
Weight $6$
Character orbit 819.y
Rep. character $\chi_{819}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $460$
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.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 1136 468 668
Cusp forms 1104 460 644
Eisenstein series 32 8 24

Trace form

\( 460 q + 4 q^{2} - 24 q^{7} - 124 q^{8} + O(q^{10}) \) \( 460 q + 4 q^{2} - 24 q^{7} - 124 q^{8} + 344 q^{11} + 2308 q^{14} - 108552 q^{16} + 4760 q^{22} - 4644 q^{28} - 620 q^{29} + 11056 q^{32} + 28132 q^{35} - 13876 q^{37} + 28116 q^{44} + 103656 q^{46} - 54692 q^{50} + 66156 q^{53} + 131524 q^{58} - 120080 q^{65} - 190516 q^{67} - 89048 q^{70} + 168792 q^{71} - 242736 q^{74} + 5228 q^{79} + 47652 q^{85} + 26172 q^{86} + 119904 q^{91} - 89256 q^{92} - 328436 q^{98} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(819, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)