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

• Label: 296.2.e
• Level: $296$
• Weight: $2$
• Character orbit: 296.e
• Rep. character: $\chi_{296}(221,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $1$
• Sturm bound: $76$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 296 = 2^{3} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	296.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 296 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(76\)
Trace bound:			\(0\)

Dimensions

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

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

Trace form

36 * q - 4 * q^4 - 8 * q^7 - 36 * q^9 - 6 * q^10 - 6 * q^12 - 12 * q^16 + 20 * q^25 + 10 * q^26 - 28 * q^28 - 40 * q^30 + 8 * q^33 + 4 * q^34 - 10 * q^36 - 24 * q^38 + 30 * q^40 + 34 * q^44 + 26 * q^46 + 16 * q^47 - 2 * q^48 + 36 * q^49 + 38 * q^58 - 14 * q^62 + 40 * q^63 + 20 * q^64 - 48 * q^65 - 20 * q^70 - 24 * q^71 - 8 * q^73 + 12 * q^74 + 42 * q^78 + 28 * q^81 - 84 * q^84 + 48 * q^86 + 36 * q^90 - 56 * q^95

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.e.a	$296$	$2$	296.e	296.e	$2$	$36$	$36$	$2.364$		None		✓	✓	✓	296.2.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{2}]$