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Properties

Label 693.6.m
Level $693$
Weight $6$
Character orbit 693.m
Rep. character $\chi_{693}(64,\cdot)$
Character field $\Q(\zeta_{5})$
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.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 1952 600 1352
Cusp forms 1888 600 1288
Eisenstein series 64 0 64

Trace form

\( 600 q + 10 q^{2} - 2378 q^{4} - 58 q^{5} - 98 q^{7} + 110 q^{8} + O(q^{10}) \) \( 600 q + 10 q^{2} - 2378 q^{4} - 58 q^{5} - 98 q^{7} + 110 q^{8} + 1136 q^{10} + 1282 q^{11} + 442 q^{13} + 1617 q^{14} - 32218 q^{16} - 1568 q^{17} - 830 q^{19} + 6518 q^{20} - 820 q^{22} - 6736 q^{23} - 85440 q^{25} - 16446 q^{26} - 5929 q^{28} + 4938 q^{29} + 8094 q^{31} - 21600 q^{32} + 5412 q^{34} + 9800 q^{35} - 9698 q^{37} + 18486 q^{38} + 120310 q^{40} - 46384 q^{41} + 12296 q^{43} - 62937 q^{44} + 115745 q^{46} - 24680 q^{47} - 360150 q^{49} - 30384 q^{50} - 311778 q^{52} - 39750 q^{53} - 7090 q^{55} + 3234 q^{56} + 373799 q^{58} + 149826 q^{59} - 59088 q^{61} - 236726 q^{62} - 348994 q^{64} - 298456 q^{65} - 316196 q^{67} - 92082 q^{68} - 18620 q^{70} + 147424 q^{71} - 5480 q^{73} + 10802 q^{74} + 727236 q^{76} + 15680 q^{77} - 68370 q^{79} - 867108 q^{80} - 454864 q^{82} - 26044 q^{83} - 329452 q^{85} - 19449 q^{86} + 212520 q^{88} + 981680 q^{89} - 48510 q^{91} + 1104779 q^{92} - 209490 q^{94} - 163880 q^{95} - 703678 q^{97} - 72030 q^{98} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)