Space of modular forms of level 1232, weight 2, and Character 1232.bi

• Label: 1232.2.bi
• Level: $1232$
• Weight: $2$
• Character orbit: 1232.bi
• Rep. character: $\chi_{1232}(527,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $3$
• Sturm bound: $384$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.bi (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 308 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(384\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1232, [\chi])\).

	Total	New	Old
Modular forms	408	96	312
Cusp forms	360	96	264
Eisenstein series	48	0	48

Trace form

\( 96 q + 48 q^{9} - 24 q^{25} + 12 q^{33} - 24 q^{49} + 24 q^{53} + 96 q^{69} - 72 q^{77} - 48 q^{81} + 48 q^{89} + 48 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1232, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1232.2.bi.a	$1232$	$2$	1232.bi	308.n	$6$	$32$	$16$	$9.838$		None		✓			1232.2.bi.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1232.2.bi.b	$1232$	$2$	1232.bi	308.n	$6$	$32$	$16$	$9.838$		None		✓			1232.2.bi.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1232.2.bi.c	$1232$	$2$	1232.bi	308.n	$6$	$32$	$16$	$9.838$		None		✓			1232.2.bi.c	$8$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1232, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1232, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 3}\)