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Properties

Label 684.5.bw
Level $684$
Weight $5$
Character orbit 684.bw
Rep. character $\chi_{684}(5,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $480$
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.bw (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
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 2916 480 2436
Cusp forms 2844 480 2364
Eisenstein series 72 0 72

Trace form

\( 480 q + 24 q^{3} + 168 q^{9} + O(q^{10}) \) \( 480 q + 24 q^{3} + 168 q^{9} - 15 q^{13} - 102 q^{15} + 2025 q^{17} - 231 q^{19} + 2160 q^{23} + 1380 q^{27} + 1950 q^{33} - 1740 q^{39} + 1056 q^{43} - 2394 q^{45} - 82320 q^{49} + 1155 q^{51} + 30462 q^{57} - 14715 q^{59} + 2541 q^{61} + 1452 q^{63} + 7266 q^{67} + 7254 q^{69} + 19371 q^{73} - 13362 q^{79} - 64284 q^{81} - 16956 q^{83} + 35484 q^{87} - 22032 q^{89} - 14208 q^{91} - 120 q^{93} - 29808 q^{95} - 16920 q^{97} + 26754 q^{99} + O(q^{100}) \)

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

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