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Properties

Label 693.6.i
Level $693$
Weight $6$
Character orbit 693.i
Rep. character $\chi_{693}(100,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $332$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
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 976 332 644
Cusp forms 944 332 612
Eisenstein series 32 0 32

Trace form

\( 332 q - 2624 q^{4} + 100 q^{5} + 94 q^{7} - 492 q^{8} + O(q^{10}) \) \( 332 q - 2624 q^{4} + 100 q^{5} + 94 q^{7} - 492 q^{8} - 534 q^{10} - 888 q^{13} + 1764 q^{14} - 41340 q^{16} + 534 q^{17} - 3498 q^{19} - 9136 q^{20} - 7116 q^{23} - 101374 q^{25} + 20062 q^{26} - 16272 q^{28} - 35592 q^{29} - 26210 q^{31} + 7092 q^{32} + 4360 q^{34} + 24822 q^{35} + 14000 q^{37} + 59912 q^{38} - 106836 q^{40} + 6520 q^{41} + 36236 q^{43} + 2420 q^{44} + 9442 q^{46} + 34542 q^{47} + 68756 q^{49} + 53592 q^{50} - 42718 q^{52} + 9410 q^{53} + 48400 q^{55} + 188802 q^{56} + 125782 q^{58} + 55016 q^{59} + 56476 q^{61} - 254396 q^{62} + 1133148 q^{64} - 4470 q^{65} - 226900 q^{67} + 10964 q^{68} + 359538 q^{70} + 341668 q^{71} + 90054 q^{73} + 258868 q^{74} + 507448 q^{76} + 14762 q^{77} - 77348 q^{79} - 13038 q^{80} + 141910 q^{82} - 723884 q^{83} - 276752 q^{85} - 300810 q^{86} - 114708 q^{88} + 245122 q^{89} + 303574 q^{91} + 1143940 q^{92} + 457126 q^{94} + 442936 q^{95} + 723268 q^{97} - 873666 q^{98} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)