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Properties

Label 1216.1.p
Level $1216$
Weight $1$
Character orbit 1216.p
Rep. character $\chi_{1216}(673,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
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.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{6})\)
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 28 4 24
Cusp forms 4 4 0
Eisenstein series 24 0 24

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4q - 4q^{9} + O(q^{10}) \) \( 4q - 4q^{9} - 4q^{17} - 2q^{25} - 6q^{33} + 6q^{41} - 4q^{49} - 2q^{73} - 2q^{81} + 6q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.p.a \(4\) \(0.607\) \(\Q(\zeta_{12})\) \(D_{6}\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+(-1-\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)