Properties

Label 864.1.bd
Level $864$
Weight $1$
Character orbit 864.bd
Rep. character $\chi_{864}(79,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $6$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 864.bd (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 216 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(864, [\chi])\).

Total New Old
Modular forms 72 18 54
Cusp forms 24 6 18
Eisenstein series 48 12 36

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 6 0 0 0

Trace form

\( 6 q + O(q^{10}) \) \( 6 q + 3 q^{11} + 3 q^{27} - 3 q^{33} - 3 q^{41} + 3 q^{43} - 6 q^{51} - 3 q^{57} - 6 q^{59} + 3 q^{67} + 3 q^{89} - 3 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(864, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
864.1.bd.a \(6\) \(0.431\) \(\Q(\zeta_{18})\) \(D_{9}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}q^{3}+\zeta_{18}^{2}q^{9}+(\zeta_{18}^{5}-\zeta_{18}^{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(864, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(864, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 3}\)