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Properties

Label 864.2.bf
Level $864$
Weight $2$
Character orbit 864.bf
Rep. character $\chi_{864}(49,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $204$
Newform subspaces $1$
Sturm bound $288$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.bf (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 216 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(288\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(864, [\chi])\).

Total New Old
Modular forms 912 228 684
Cusp forms 816 204 612
Eisenstein series 96 24 72

Trace form

\( 204 q + 12 q^{7} - 12 q^{9} + O(q^{10}) \) \( 204 q + 12 q^{7} - 12 q^{9} + 12 q^{15} - 6 q^{17} + 12 q^{23} - 12 q^{25} + 12 q^{31} + 12 q^{39} - 24 q^{41} + 12 q^{47} - 12 q^{49} + 24 q^{55} - 30 q^{57} + 72 q^{63} - 12 q^{65} + 90 q^{71} - 6 q^{73} + 12 q^{79} - 12 q^{81} + 48 q^{87} - 6 q^{89} + 42 q^{95} - 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(864, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
864.2.bf.a 864.bf 216.t $204$ $6.899$ None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(432, [\chi])\)\(^{\oplus 2}\)