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Properties

Label 819.6.ej
Level $819$
Weight $6$
Character orbit 819.ej
Rep. character $\chi_{819}(335,\cdot)$
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.ej (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

\( 1112 q - 12 q^{2} + 17660 q^{4} - 3 q^{7} - 384 q^{8} + 108 q^{9} + O(q^{10}) \) \( 1112 q - 12 q^{2} + 17660 q^{4} - 3 q^{7} - 384 q^{8} + 108 q^{9} - 12 q^{11} - 6 q^{14} + 1644 q^{15} + 278396 q^{16} - 624 q^{18} + 729 q^{21} - 516 q^{22} + 7902 q^{23} + 337496 q^{25} - 102 q^{28} + 7724 q^{30} - 12300 q^{32} + 26622 q^{35} + 22562 q^{36} - 15486 q^{37} + 4080 q^{39} - 24765 q^{42} - 18486 q^{43} - 12672 q^{44} - 12 q^{46} + 12239 q^{49} - 38388 q^{50} + 36892 q^{51} - 50616 q^{56} + 92916 q^{57} + 97806 q^{60} - 65793 q^{63} + 4321136 q^{64} + 172986 q^{65} - 3744 q^{67} + 50325 q^{70} + 53592 q^{71} - 223494 q^{72} - 58128 q^{74} + 133614 q^{77} - 100202 q^{78} + 6504 q^{79} + 56460 q^{81} + 20253 q^{84} + 571044 q^{86} - 147588 q^{88} + 38250 q^{91} + 560040 q^{92} - 788742 q^{93} - 337614 q^{99} + O(q^{100}) \)

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.