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

• Label: 296.2.c
• Level: $296$
• Weight: $2$
• Character orbit: 296.c
• Rep. character: $\chi_{296}(149,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• 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.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(76\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	40	36	4
Cusp forms	36	36	0
Eisenstein series	4	0	4

Trace form

\( 36 q - 4 q^{4} + 2 q^{6} - 36 q^{9} + O(q^{10}) \)

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.c.a	$296$	$2$	296.c	8.b	$2$	$4$	$4$	$2.364$	\(\Q(i, \sqrt{29})\)	None		✓			296.2.c.a	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+\cdots\)
296.2.c.b	$296$	$2$	296.c	8.b	$2$	$4$	$4$	$2.364$	\(\Q(i, \sqrt{5})\)	None		✓			296.2.c.b	$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{3})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+2\beta _{3}q^{4}+\cdots\)
296.2.c.c	$296$	$2$	296.c	8.b	$2$	$28$	$28$	$2.364$		None		✓	✓		296.2.c.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$