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Properties

Label 684.5.t
Level $684$
Weight $5$
Character orbit 684.t
Rep. character $\chi_{684}(265,\cdot)$
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.t (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

\( 160 q - 26 q^{7} - 56 q^{9} + O(q^{10}) \) \( 160 q - 26 q^{7} - 56 q^{9} + 168 q^{11} + 948 q^{17} - 562 q^{19} + 480 q^{23} - 10000 q^{25} - 2376 q^{35} + 2046 q^{39} + 1544 q^{43} + 2078 q^{45} + 6042 q^{47} - 29286 q^{49} - 5979 q^{57} - 1694 q^{61} - 15502 q^{63} - 22420 q^{73} - 4260 q^{77} - 43424 q^{81} + 18570 q^{83} - 39888 q^{87} - 35748 q^{93} - 4572 q^{95} + 13850 q^{99} + O(q^{100}) \)

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

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