Properties

Label 684.3.bx
Level $684$
Weight $3$
Character orbit 684.bx
Rep. character $\chi_{684}(109,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $102$
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.bx (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
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 1512 102 1410
Cusp forms 1368 102 1266
Eisenstein series 144 0 144

Trace form

\( 102q + 9q^{7} + O(q^{10}) \) \( 102q + 9q^{7} - 15q^{11} + 9q^{13} + 9q^{17} + 12q^{19} - 96q^{23} + 18q^{25} - 93q^{29} - 108q^{31} - 111q^{35} + 18q^{41} + 117q^{43} + 15q^{47} - 342q^{49} - 75q^{53} - 3q^{55} + 165q^{59} + 132q^{61} + 225q^{65} + 531q^{67} + 90q^{71} - 90q^{73} + 108q^{77} + 39q^{79} + 207q^{83} - 234q^{85} + 168q^{89} + 402q^{91} + 393q^{95} + 279q^{97} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)