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Properties

Label 684.5.bx
Level $684$
Weight $5$
Character orbit 684.bx
Rep. character $\chi_{684}(109,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $198$
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.bx (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
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 2952 198 2754
Cusp forms 2808 198 2610
Eisenstein series 144 0 144

Trace form

\( 198 q - 45 q^{7} + O(q^{10}) \) \( 198 q - 45 q^{7} - 45 q^{11} - 93 q^{13} - 441 q^{17} - 780 q^{19} + 1080 q^{23} + 2286 q^{25} - 243 q^{29} + 2808 q^{31} + 4959 q^{35} - 1404 q^{41} - 4209 q^{43} + 1557 q^{47} - 27492 q^{49} + 7263 q^{53} + 831 q^{55} - 23967 q^{59} - 16200 q^{61} - 14445 q^{65} - 22029 q^{67} + 32490 q^{71} + 13242 q^{73} + 12924 q^{77} + 10029 q^{79} + 4941 q^{83} - 558 q^{85} - 7956 q^{89} + 29574 q^{91} + 53235 q^{95} + 53199 q^{97} + O(q^{100}) \)

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

\( S_{5}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)