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

• Label: 296.2.bj
• Level: $296$
• Weight: $2$
• Character orbit: 296.bj
• Rep. character: $\chi_{296}(19,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $432$
• 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.bj (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 296 \)
Character field:			\(\Q(\zeta_{36})\)
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	480	480	0
Cusp forms	432	432	0
Eisenstein series	48	48	0

Trace form

432 * q - 12 * q^2 - 24 * q^3 - 18 * q^4 - 12 * q^6 - 6 * q^8 - 24 * q^9 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^14 + 18 * q^16 - 24 * q^17 - 42 * q^18 - 24 * q^19 - 12 * q^20 - 24 * q^22 - 84 * q^24 - 12 * q^25 - 6 * q^26 - 36 * q^27 - 12 * q^28 - 36 * q^30 - 42 * q^32 - 60 * q^33 - 12 * q^34 - 24 * q^35 + 60 * q^38 - 12 * q^40 - 24 * q^41 - 12 * q^42 - 6 * q^44 + 48 * q^46 - 18 * q^48 + 24 * q^49 - 42 * q^50 + 96 * q^51 - 42 * q^52 - 72 * q^54 - 12 * q^56 - 24 * q^57 + 48 * q^58 - 24 * q^59 + 144 * q^60 - 72 * q^62 + 108 * q^64 - 84 * q^65 - 168 * q^66 - 24 * q^67 - 18 * q^68 - 186 * q^70 + 234 * q^72 - 150 * q^74 - 48 * q^75 + 42 * q^76 - 222 * q^78 + 120 * q^80 - 60 * q^81 - 24 * q^82 - 24 * q^83 + 126 * q^84 - 54 * q^86 - 24 * q^89 + 72 * q^90 - 24 * q^91 + 114 * q^92 - 24 * q^94 + 72 * q^96 - 24 * q^97 - 114 * q^98 - 132 * q^99

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.bj.a	$296$	$2$	296.bj	296.aj	$36$	$432$	$36$	$2.364$		None		✓	✓	✓	296.2.bj.a	$4$	$0$	\(-12\)	\(-24\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$