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Properties

Label 684.3.cj
Level $684$
Weight $3$
Character orbit 684.cj
Rep. character $\chi_{684}(13,\cdot)$
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.cj (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

\( 240 q - 6 q^{3} + 6 q^{9} + O(q^{10}) \) \( 240 q - 6 q^{3} + 6 q^{9} - 15 q^{13} - 15 q^{15} + 27 q^{17} + 21 q^{19} + 144 q^{23} - 90 q^{27} - 27 q^{29} + 57 q^{33} + 162 q^{35} - 24 q^{39} - 18 q^{41} + 96 q^{43} + 243 q^{45} - 162 q^{47} + 1680 q^{49} + 9 q^{51} - 72 q^{53} + 114 q^{57} + 513 q^{59} - 42 q^{61} - 60 q^{63} + 810 q^{65} - 21 q^{67} + 351 q^{69} + 486 q^{71} - 111 q^{73} - 51 q^{79} - 318 q^{81} + 72 q^{83} + 792 q^{87} - 216 q^{89} + 192 q^{91} + 408 q^{93} + 864 q^{95} + 90 q^{97} + 633 q^{99} + O(q^{100}) \)

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

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