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Properties

Label 693.6.bz
Level $693$
Weight $6$
Character orbit 693.bz
Rep. character $\chi_{693}(148,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $2880$
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.bz (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 3872 2880 992
Cusp forms 3808 2880 928
Eisenstein series 64 0 64

Trace form

\( 2880 q + 16 q^{2} - 42 q^{3} + 5760 q^{4} + 58 q^{5} - 24 q^{6} - 1536 q^{8} + 590 q^{9} + O(q^{10}) \) \( 2880 q + 16 q^{2} - 42 q^{3} + 5760 q^{4} + 58 q^{5} - 24 q^{6} - 1536 q^{8} + 590 q^{9} - 268 q^{11} + 3712 q^{12} - 1946 q^{15} + 92160 q^{16} - 6024 q^{17} + 11568 q^{18} - 5364 q^{19} + 3712 q^{20} - 980 q^{21} + 1896 q^{22} - 24016 q^{23} + 15008 q^{24} + 221694 q^{25} + 3520 q^{26} - 30864 q^{27} + 25526 q^{29} + 26384 q^{30} + 4434 q^{31} - 114688 q^{32} - 55822 q^{33} + 15312 q^{34} - 39200 q^{35} + 90096 q^{36} - 20028 q^{37} - 72160 q^{38} + 36058 q^{39} + 40628 q^{41} + 12612 q^{43} - 59712 q^{44} - 61336 q^{45} - 84752 q^{47} - 89088 q^{48} + 864360 q^{49} + 70000 q^{50} - 82954 q^{51} - 64760 q^{53} + 435632 q^{54} + 151924 q^{57} - 95552 q^{59} + 112268 q^{60} - 405180 q^{62} - 2949120 q^{64} - 509844 q^{65} - 380348 q^{66} - 64164 q^{67} + 336230 q^{68} - 175002 q^{69} - 92540 q^{71} + 476266 q^{72} + 321768 q^{73} + 258080 q^{74} + 622620 q^{75} - 85824 q^{76} + 711624 q^{78} - 72060 q^{79} + 967600 q^{80} + 471294 q^{81} - 334224 q^{82} - 316306 q^{83} - 188160 q^{84} - 17700 q^{85} - 1095936 q^{86} + 146180 q^{87} - 627168 q^{88} - 2185912 q^{89} - 1826532 q^{90} + 97020 q^{91} - 76380 q^{92} + 512854 q^{93} + 115728 q^{94} + 734584 q^{95} + 3141956 q^{96} - 576300 q^{97} + 307328 q^{98} - 1763302 q^{99} + O(q^{100}) \)

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

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