Properties

Label 1216.1.bi
Level $1216$
Weight $1$
Character orbit 1216.bi
Rep. character $\chi_{1216}(33,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $12$
Newform subspaces $1$
Sturm bound $160$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1216.bi (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(160\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1216, [\chi])\).

Total New Old
Modular forms 84 12 72
Cusp forms 12 12 0
Eisenstein series 72 0 72

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12q + 6q^{9} + O(q^{10}) \) \( 12q + 6q^{9} + 6q^{33} - 6q^{41} + 6q^{49} - 12q^{73} - 18q^{81} - 6q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1216.1.bi.a \(12\) \(0.607\) \(\Q(\zeta_{36})\) \(D_{18}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{36}^{13}+\zeta_{36}^{15})q^{3}+(-\zeta_{36}^{8}-\zeta_{36}^{10}+\cdots)q^{9}+\cdots\)