Properties

Label 1216.1.q
Level $1216$
Weight $1$
Character orbit 1216.q
Rep. character $\chi_{1216}(767,\cdot)$
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.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
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 36 8 28
Cusp forms 12 4 8
Eisenstein series 24 4 20

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

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

Trace form

\( 4q - 2q^{5} + O(q^{10}) \) \( 4q - 2q^{5} + 2q^{13} - 2q^{17} + 2q^{29} - 2q^{41} + 4q^{49} - 2q^{53} - 2q^{57} - 2q^{61} - 4q^{65} + 4q^{69} + 2q^{73} + 2q^{81} - 2q^{85} - 2q^{89} + 4q^{93} - 2q^{97} + O(q^{100}) \)

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.q.a \(4\) \(0.607\) \(\Q(\zeta_{12})\) \(A_{4}\) None None \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{2}q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)