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Properties

Label 684.3.bw
Level $684$
Weight $3$
Character orbit 684.bw
Rep. character $\chi_{684}(5,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $240$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.bw (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(684, [\chi])\).

Total New Old
Modular forms 1476 240 1236
Cusp forms 1404 240 1164
Eisenstein series 72 0 72

Trace form

\( 240 q - 12 q^{3} - 12 q^{9} + O(q^{10}) \) \( 240 q - 12 q^{3} - 12 q^{9} + 15 q^{13} + 6 q^{15} - 81 q^{17} - 21 q^{19} - 216 q^{23} + 30 q^{27} + 78 q^{33} + 24 q^{39} - 48 q^{43} - 342 q^{45} - 840 q^{49} + 93 q^{51} - 678 q^{57} + 135 q^{59} - 21 q^{61} + 12 q^{63} - 462 q^{67} + 234 q^{69} - 183 q^{73} - 102 q^{79} + 768 q^{81} + 108 q^{83} + 24 q^{87} + 648 q^{89} - 192 q^{91} - 408 q^{93} + 648 q^{95} + 180 q^{97} - 192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(684, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{3}^{\mathrm{old}}(684, [\chi])\) into lower level spaces

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