↑

Properties

Label 684.3.q
Level $684$
Weight $3$
Character orbit 684.q
Rep. character $\chi_{684}(163,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $196$
Sturm bound $360$

Related objects

Downloads

Learn more

Defining parameters

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

Dimensions

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

Total New Old
Modular forms 496 204 292
Cusp forms 464 196 268
Eisenstein series 32 8 24

Trace form

\( 196 q + q^{2} + q^{4} + 2 q^{5} + 10 q^{8} + O(q^{10}) \) \( 196 q + q^{2} + q^{4} + 2 q^{5} + 10 q^{8} - 12 q^{10} - 10 q^{13} + 12 q^{14} - 15 q^{16} + 26 q^{17} - 48 q^{20} + 33 q^{22} - 452 q^{25} - 16 q^{26} - 42 q^{28} + 2 q^{29} + 21 q^{32} - 48 q^{34} + 72 q^{37} - 108 q^{38} - 10 q^{40} - 66 q^{41} - 15 q^{44} + 292 q^{46} - 1308 q^{49} + 310 q^{50} + 26 q^{52} + 10 q^{53} - 468 q^{56} - 240 q^{58} + 94 q^{61} + 234 q^{62} - 26 q^{64} - 156 q^{65} + 84 q^{68} + 108 q^{70} + 106 q^{73} + 72 q^{74} - 345 q^{76} - 416 q^{77} + 32 q^{80} - 73 q^{82} - 6 q^{85} + 148 q^{86} + 922 q^{88} - 22 q^{89} + 378 q^{92} - 664 q^{94} + 298 q^{97} + 309 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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