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

• Label: 296.2.j
• Level: $296$
• Weight: $2$
• Character orbit: 296.j
• Rep. character: $\chi_{296}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $76$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 296 = 2^{3} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	296.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 296 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(76\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	80	80	0
Cusp forms	72	72	0
Eisenstein series	8	8	0

Trace form

\( 72 q - 4 q^{2} + 2 q^{6} - 4 q^{8} - 72 q^{9} + O(q^{10}) \)

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.j.a	$296$	$2$	296.j	296.j	$4$	$8$	$4$	$2.364$	8.0.\(\cdots\).12	None		✓			296.2.j.a	$4$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{2})q^{2}+(-\beta _{2}-\beta _{6})q^{3}-2\beta _{2}q^{4}+\cdots\)
296.2.j.b	$296$	$2$	296.j	296.j	$4$	$64$	$32$	$2.364$		None		✓	✓		296.2.j.b	$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$