Properties

Label 684.3.cg
Level $684$
Weight $3$
Character orbit 684.cg
Rep. character $\chi_{684}(55,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $588$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.cg (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(684, [\chi])\).

Total New Old
Modular forms 1488 612 876
Cusp forms 1392 588 804
Eisenstein series 96 24 72

Trace form

\( 588q + 6q^{2} - 12q^{4} + 12q^{5} + 3q^{8} + O(q^{10}) \) \( 588q + 6q^{2} - 12q^{4} + 12q^{5} + 3q^{8} + 51q^{10} + 12q^{13} - 27q^{14} + 36q^{16} + 12q^{17} + 42q^{20} - 18q^{22} - 12q^{25} - 69q^{26} - 216q^{28} + 12q^{29} - 249q^{32} - 108q^{34} - 24q^{37} + 252q^{38} + 330q^{40} + 216q^{41} + 363q^{44} + 132q^{46} + 1800q^{49} + 120q^{50} + 9q^{52} - 12q^{53} + 306q^{56} + 60q^{58} + 396q^{61} + 468q^{62} + 75q^{64} - 114q^{65} + 240q^{68} - 765q^{70} - 444q^{73} - 363q^{74} + 570q^{76} + 756q^{77} + 69q^{80} + 183q^{82} - 924q^{85} - 768q^{86} - 75q^{88} + 372q^{89} - 1092q^{92} + 1074q^{94} + 96q^{97} + 603q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(684, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(684, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)