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Properties

Label 693.6.ce
Level $693$
Weight $6$
Character orbit 693.ce
Rep. character $\chi_{693}(47,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $3808$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 693.ce (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 693 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(693, [\chi])\).

Total New Old
Modular forms 3872 3872 0
Cusp forms 3808 3808 0
Eisenstein series 64 64 0

Trace form

\( 3808 q - 9 q^{2} - 9 q^{3} - 7549 q^{4} - 18 q^{5} + 192 q^{6} - 3 q^{7} + 327 q^{9} + O(q^{10}) \) \( 3808 q - 9 q^{2} - 9 q^{3} - 7549 q^{4} - 18 q^{5} + 192 q^{6} - 3 q^{7} + 327 q^{9} - 48 q^{10} - 24 q^{12} - 9 q^{14} - 1176 q^{15} + 118851 q^{16} + 1117 q^{18} - 18 q^{19} - 288 q^{20} - 774 q^{21} - 72 q^{22} - 1467 q^{24} - 575006 q^{25} - 29904 q^{26} - 18117 q^{27} + 1972 q^{28} - 18 q^{29} + 4917 q^{30} - 9 q^{31} - 6168 q^{32} - 45660 q^{33} + 192 q^{34} + 34995 q^{35} + 39832 q^{36} - 6 q^{37} - 29958 q^{38} - 9561 q^{39} + 107109 q^{42} - 16 q^{43} - 69885 q^{44} - 24 q^{45} + 186 q^{46} - 9 q^{47} + 7950 q^{48} - 3 q^{49} + 48849 q^{50} + 23239 q^{51} - 23364 q^{53} - 231444 q^{54} + 42354 q^{56} + 56546 q^{57} + 30346 q^{58} + 59061 q^{59} + 111593 q^{60} - 9 q^{61} + 384 q^{62} - 33857 q^{63} + 3674280 q^{64} + 131676 q^{65} + 533940 q^{66} + 8 q^{67} - 18 q^{68} + 2187 q^{69} + 128874 q^{70} + 279601 q^{72} - 18 q^{73} - 96429 q^{75} - 5760 q^{76} - 553029 q^{77} + 479836 q^{78} + 17451 q^{79} - 6144 q^{80} + 231331 q^{81} - 210 q^{82} - 113829 q^{84} - 23956 q^{85} - 1385814 q^{87} - 69512 q^{88} - 45870 q^{89} + 18462 q^{90} + 67216 q^{91} + 109128 q^{92} + 586963 q^{93} - 9 q^{94} + 508443 q^{95} + 294903 q^{96} - 575616 q^{98} - 615880 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(693, [\chi])\) into newform subspaces

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