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Properties

Label 693.6.ba
Level $693$
Weight $6$
Character orbit 693.ba
Rep. character $\chi_{693}(439,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $952$
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.ba (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 693 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

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

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

Trace form

\( 952 q - 6 q^{3} + 7554 q^{4} - 222 q^{9} + O(q^{10}) \) \( 952 q - 6 q^{3} + 7554 q^{4} - 222 q^{9} + 378 q^{11} - 6 q^{12} - 130 q^{14} + 1578 q^{15} - 118846 q^{16} + 12096 q^{20} + 62 q^{22} + 128 q^{23} - 575004 q^{25} + 20244 q^{26} - 12078 q^{27} - 6 q^{31} - 28680 q^{33} - 192 q^{34} + 35868 q^{36} - 4 q^{37} - 42398 q^{42} + 19197 q^{44} - 6 q^{45} - 6 q^{47} + 7410 q^{48} - 2 q^{49} - 75376 q^{53} - 71120 q^{56} - 20324 q^{58} - 59076 q^{59} + 147000 q^{60} - 3674000 q^{64} - 141987 q^{66} + 2 q^{67} - 1458 q^{69} - 62072 q^{70} + 199216 q^{71} - 96426 q^{75} - 111316 q^{77} + 73310 q^{78} + 387060 q^{80} + 240946 q^{81} + 180 q^{82} + 9276 q^{86} + 69502 q^{88} - 45882 q^{89} + 67220 q^{91} - 30050 q^{92} + 395446 q^{93} - 692204 q^{99} + O(q^{100}) \)

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.