Space of modular forms of level 296, weight 2, and Character 296.y

• Label: 296.2.y
• Level: $296$
• Weight: $2$
• Character orbit: 296.y
• Rep. character: $\chi_{296}(51,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $144$
• Newform subspaces: $3$
• Sturm bound: $76$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 296 = 2^{3} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	296.y (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 296 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(76\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(296, [\chi])\).

	Total	New	Old
Modular forms	160	160	0
Cusp forms	144	144	0
Eisenstein series	16	16	0

Trace form

\( 144 q - 2 q^{2} - 12 q^{3} - 8 q^{6} - 8 q^{8} + 60 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(296, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
296.2.y.a	$296$	$2$	296.y	296.y	$12$	$4$	$1$	$2.364$	\(\Q(\zeta_{12})\)	None		✓			296.2.y.a	$2$	$1$	\(-4\)	\(-6\)	\(-2\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+\zeta_{12}^{3})q^{2}+(-1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
296.2.y.b	$296$	$2$	296.y	296.y	$12$	$4$	$1$	$2.364$	\(\Q(\zeta_{12})\)	None		✓			296.2.y.a	$2$	$0$	\(2\)	\(-6\)	\(2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1-\zeta_{12}+\cdots)q^{3}+\cdots\)
296.2.y.c	$296$	$2$	296.y	296.y	$12$	$136$	$34$	$2.364$		None		✓	✓		296.2.y.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$