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Properties

Label 684.2.bv
Level $684$
Weight $2$
Character orbit 684.bv
Rep. character $\chi_{684}(29,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $120$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 684.bv (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(684, [\chi])\).

Total New Old
Modular forms 756 120 636
Cusp forms 684 120 564
Eisenstein series 72 0 72

Trace form

\( 120 q - 6 q^{3} + 6 q^{9} + O(q^{10}) \) \( 120 q - 6 q^{3} + 6 q^{9} - 3 q^{13} - 6 q^{15} + 27 q^{17} - 3 q^{19} + 36 q^{23} - 9 q^{27} - 6 q^{33} + 30 q^{39} - 6 q^{43} - 60 q^{49} + 9 q^{51} + 24 q^{57} + 45 q^{59} - 21 q^{61} + 30 q^{63} - 24 q^{67} + 39 q^{73} + 6 q^{79} + 42 q^{81} + 36 q^{83} + 54 q^{87} - 54 q^{89} - 12 q^{91} - 78 q^{93} - 54 q^{95} + 18 q^{97} - 51 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(684, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
684.2.bv.a 684.bv 171.x $120$ $5.462$ None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(684, [\chi])\) into lower level spaces

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