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Properties

Label 684.5.be
Level $684$
Weight $5$
Character orbit 684.be
Rep. character $\chi_{684}(425,\cdot)$
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.be (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

\( 160 q - 8 q^{3} - 13 q^{7} - 56 q^{9} + O(q^{10}) \) \( 160 q - 8 q^{3} - 13 q^{7} - 56 q^{9} + 252 q^{11} - 10 q^{13} + 295 q^{15} + 747 q^{17} - 50 q^{19} + 510 q^{21} + 10000 q^{25} + 1627 q^{27} + 1323 q^{29} + 368 q^{31} - 2743 q^{33} + 1034 q^{37} - 15 q^{39} + 4428 q^{41} + 2384 q^{43} - 1612 q^{45} - 13914 q^{47} - 26517 q^{49} + 8530 q^{51} - 3492 q^{53} + 414 q^{57} - 15237 q^{59} - 847 q^{61} + 7498 q^{63} - 9792 q^{65} - 2422 q^{67} - 2668 q^{69} + 11205 q^{71} - 3901 q^{73} + 225 q^{75} + 7560 q^{77} + 4454 q^{79} + 21424 q^{81} - 2313 q^{83} + 38048 q^{87} + 7344 q^{89} - 11762 q^{91} - 14216 q^{93} + 43956 q^{95} + 18332 q^{97} + 1423 q^{99} + O(q^{100}) \)

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

\( S_{5}^{\mathrm{old}}(684, [\chi]) \cong \)