Properties

Label 684.5.cg
Level $684$
Weight $5$
Character orbit 684.cg
Rep. character $\chi_{684}(55,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $1188$
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.cg (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
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 2928 1212 1716
Cusp forms 2832 1188 1644
Eisenstein series 96 24 72

Trace form

\( 1188 q + 6 q^{2} + 36 q^{4} + 12 q^{5} + 3 q^{8} + O(q^{10}) \) \( 1188 q + 6 q^{2} + 36 q^{4} + 12 q^{5} + 3 q^{8} - 153 q^{10} - 540 q^{13} + 189 q^{14} + 708 q^{16} + 12 q^{17} - 1158 q^{20} - 54 q^{22} - 12 q^{25} + 3099 q^{26} - 4824 q^{28} + 12 q^{29} + 7431 q^{32} + 6108 q^{34} - 24 q^{37} - 1524 q^{38} - 6942 q^{40} - 10140 q^{41} - 15237 q^{44} - 1488 q^{46} + 191388 q^{49} + 8076 q^{50} + 6369 q^{52} + 2460 q^{53} + 14418 q^{56} - 8292 q^{58} + 18660 q^{61} + 27504 q^{62} + 5499 q^{64} + 3606 q^{65} - 22776 q^{68} + 57123 q^{70} + 26772 q^{73} - 13695 q^{74} - 43206 q^{76} + 7236 q^{77} + 30093 q^{80} + 14259 q^{82} + 59220 q^{85} + 72024 q^{86} - 26763 q^{88} + 1884 q^{89} + 13740 q^{92} + 102186 q^{94} - 5556 q^{97} + 19527 q^{98} + O(q^{100}) \)

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

\( S_{5}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)