Space of modular forms of level 1216, weight 1, and Character 1216.g

• Label: 1216.1.g
• Level: $1216$
• Weight: $1$
• Character orbit: 1216.g
• Rep. character: $\chi_{1216}(417,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $160$
• Trace bound: $1$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	30	6	24
Cusp forms	18	6	12
Eisenstein series	12	0	12

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

\( 6 q - 6 q^{9} + O(q^{10}) \)

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1216.1.g.a	$1216$	$1$	1216.g	152.g	$2$	$2$	$2$	$0.607$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{38}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{9}-iq^{11}+q^{17}-iq^{19}+q^{25}+\cdots\)
1216.1.g.b	$1216$	$1$	1216.g	152.g	$2$	$4$	$4$	$0.607$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-19}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{5}+(\zeta_{12}-\zeta_{12}^{5}+\cdots)q^{7}+\cdots\)

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

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