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Properties

Label 684.5.cj
Level $684$
Weight $5$
Character orbit 684.cj
Rep. character $\chi_{684}(13,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $480$
Sturm bound $600$

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Defining parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 684.cj (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(684, [\chi])\).

Total New Old
Modular forms 2916 480 2436
Cusp forms 2844 480 2364
Eisenstein series 72 0 72

Trace form

\( 480 q + 12 q^{3} - 84 q^{9} + O(q^{10}) \) \( 480 q + 12 q^{3} - 84 q^{9} + 15 q^{13} + 363 q^{15} - 675 q^{17} + 231 q^{19} - 1440 q^{23} - 4140 q^{27} + 1323 q^{29} - 735 q^{33} + 1782 q^{35} + 1740 q^{39} + 828 q^{41} - 2112 q^{43} - 675 q^{45} + 2106 q^{47} + 164640 q^{49} - 6741 q^{51} + 6984 q^{53} - 19506 q^{57} - 21411 q^{59} + 5082 q^{61} + 9372 q^{63} - 39690 q^{65} - 19257 q^{67} + 10881 q^{69} + 9234 q^{71} + 9147 q^{73} - 6681 q^{79} + 8124 q^{81} - 11304 q^{83} - 27792 q^{87} + 7344 q^{89} + 14208 q^{91} + 69240 q^{93} + 38016 q^{95} - 8460 q^{97} - 31731 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(684, [\chi])\) into newform subspaces

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

Decomposition of \(S_{5}^{\mathrm{old}}(684, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)