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Properties

Label 693.6.j
Level $693$
Weight $6$
Character orbit 693.j
Rep. character $\chi_{693}(232,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $600$
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 968 600 368
Cusp forms 952 600 352
Eisenstein series 16 0 16

Trace form

\( 600 q + 2 q^{3} - 4800 q^{4} + 58 q^{5} + 228 q^{6} - 1704 q^{8} + 62 q^{9} + O(q^{10}) \) \( 600 q + 2 q^{3} - 4800 q^{4} + 58 q^{5} + 228 q^{6} - 1704 q^{8} + 62 q^{9} + 968 q^{11} + 3272 q^{12} + 1568 q^{14} - 4572 q^{15} - 76800 q^{16} - 16500 q^{18} + 5364 q^{20} + 23972 q^{23} - 31364 q^{24} - 190806 q^{25} - 44112 q^{26} - 1720 q^{27} - 20944 q^{30} + 4434 q^{31} + 22444 q^{32} - 15004 q^{33} + 25320 q^{34} + 10912 q^{36} - 20028 q^{37} - 68824 q^{38} - 23856 q^{39} - 18600 q^{40} - 10480 q^{41} + 80360 q^{42} - 77440 q^{44} - 41678 q^{45} + 107760 q^{46} - 41548 q^{47} - 118280 q^{48} - 720300 q^{49} - 200660 q^{50} + 87452 q^{51} - 91764 q^{52} - 176248 q^{53} + 28348 q^{54} - 27588 q^{55} + 75264 q^{56} - 23132 q^{57} + 12996 q^{58} - 135498 q^{59} + 484316 q^{60} + 228168 q^{62} + 19600 q^{63} + 2463768 q^{64} - 164384 q^{65} + 5514 q^{67} - 555256 q^{68} + 2026 q^{69} - 319660 q^{71} + 157820 q^{72} - 271880 q^{74} - 250422 q^{75} - 100680 q^{76} + 47432 q^{77} + 631392 q^{78} - 402688 q^{80} + 2518 q^{81} - 1157448 q^{82} - 75664 q^{83} - 80948 q^{84} + 163248 q^{85} + 301188 q^{86} - 1240212 q^{87} - 184168 q^{89} - 1066044 q^{90} + 633048 q^{92} + 819846 q^{93} + 369396 q^{94} + 415736 q^{95} + 123596 q^{96} - 298698 q^{97} - 114950 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{6}^{\mathrm{old}}(693, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)