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Properties

Label 684.5.s
Level $684$
Weight $5$
Character orbit 684.s
Rep. character $\chi_{684}(445,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
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.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(600\)

Dimensions

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

Total New Old
Modular forms 972 160 812
Cusp forms 948 160 788
Eisenstein series 24 0 24

Trace form

\( 160 q + 13 q^{7} - 56 q^{9} + O(q^{10}) \) \( 160 q + 13 q^{7} - 56 q^{9} - 84 q^{11} - 885 q^{15} + 201 q^{17} + 50 q^{19} + 480 q^{23} - 10000 q^{25} + 315 q^{27} + 1323 q^{29} + 1104 q^{31} - 1755 q^{33} - 594 q^{35} + 1233 q^{39} + 828 q^{41} - 976 q^{43} - 11596 q^{45} + 3936 q^{47} - 26517 q^{49} + 8568 q^{51} + 3492 q^{53} - 7254 q^{57} + 2565 q^{59} + 847 q^{61} - 2902 q^{63} + 3744 q^{65} + 1056 q^{69} + 24381 q^{71} - 5605 q^{73} - 14523 q^{75} + 2130 q^{77} - 13208 q^{81} - 6459 q^{83} - 20358 q^{87} - 7344 q^{89} + 7104 q^{91} - 32520 q^{93} + 8460 q^{95} - 12673 q^{99} + O(q^{100}) \)

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

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