Properties

Label 864.2.bf
Level 864
Weight 2
Character orbit 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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
864.2.bf.a \(204\) \(6.899\) None \(0\) \(0\) \(0\) \(12\)

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

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

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database