Properties

Label 216.1.r
Level $216$
Weight $1$
Character orbit 216.r
Rep. character $\chi_{216}(43,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $6$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 216.r (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 216 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(216, [\chi])\).

Total New Old
Modular forms 18 18 0
Cusp forms 6 6 0
Eisenstein series 12 12 0

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

\( 6q - 3q^{8} + O(q^{10}) \) \( 6q - 3q^{8} - 3q^{11} - 3q^{12} + 6q^{18} - 3q^{22} - 3q^{27} - 3q^{33} - 3q^{34} + 6q^{38} - 3q^{41} - 3q^{43} + 6q^{51} - 3q^{57} + 6q^{59} - 3q^{64} - 3q^{67} + 6q^{68} + 6q^{76} - 3q^{86} + 6q^{88} + 3q^{89} + 6q^{96} - 3q^{97} - 3q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(216, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
216.1.r.a \(6\) \(0.108\) \(\Q(\zeta_{18})\) \(D_{9}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\cdots\)