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Properties

Label 684.5.bc
Level $684$
Weight $5$
Character orbit 684.bc
Rep. character $\chi_{684}(77,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
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.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
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 972 144 828
Cusp forms 948 144 804
Eisenstein series 24 0 24

Trace form

\( 144 q + 10 q^{3} + 18 q^{5} - 98 q^{9} + O(q^{10}) \) \( 144 q + 10 q^{3} + 18 q^{5} - 98 q^{9} - 468 q^{11} + 208 q^{15} + 1314 q^{21} + 1998 q^{23} + 9294 q^{25} + 970 q^{27} - 1584 q^{29} - 1110 q^{31} - 3070 q^{33} - 2100 q^{37} + 12048 q^{39} + 8928 q^{41} + 704 q^{45} - 13464 q^{47} - 28632 q^{49} - 3800 q^{51} + 3636 q^{55} + 9630 q^{59} + 5568 q^{61} - 380 q^{63} - 32346 q^{65} - 2730 q^{67} - 30700 q^{69} + 60144 q^{75} + 36162 q^{77} + 8844 q^{79} - 6698 q^{81} - 52452 q^{83} + 6084 q^{85} - 22522 q^{87} - 22344 q^{91} + 23638 q^{93} - 15270 q^{97} + 47632 q^{99} + O(q^{100}) \)

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

\( S_{5}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)