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Properties

Label 684.3.v
Level $684$
Weight $3$
Character orbit 684.v
Rep. character $\chi_{684}(115,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $432$
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.v (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
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 488 432 56
Cusp forms 472 432 40
Eisenstein series 16 0 16

Trace form

\( 432 q + 6 q^{6} + 36 q^{8} + O(q^{10}) \) \( 432 q + 6 q^{6} + 36 q^{8} + 50 q^{12} + 30 q^{14} + 8 q^{18} + 16 q^{21} - 148 q^{24} - 1080 q^{25} - 264 q^{26} + 48 q^{29} - 60 q^{30} - 240 q^{32} + 22 q^{36} + 500 q^{42} + 288 q^{44} - 112 q^{45} + 130 q^{48} + 1512 q^{49} + 438 q^{50} + 18 q^{52} - 288 q^{53} + 116 q^{54} - 84 q^{56} - 90 q^{58} - 974 q^{60} - 360 q^{62} + 252 q^{64} - 678 q^{66} - 696 q^{68} + 64 q^{69} - 180 q^{72} + 504 q^{74} + 96 q^{77} + 1076 q^{78} + 1548 q^{80} - 80 q^{81} - 396 q^{82} + 518 q^{84} + 768 q^{86} - 24 q^{88} + 480 q^{89} - 334 q^{90} - 114 q^{92} + 928 q^{93} - 114 q^{94} - 1148 q^{96} - 1368 q^{98} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)