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 - 8 * q^10 - 14 * q^12 - 16 * q^14 - 12 * q^16 - 4 * q^17 + 10 * q^18 - 8 * q^19 - 10 * q^20 - 8 * q^22 + 22 * q^24 - 24 * q^25 - 8 * q^26 - 6 * q^28 + 18 * q^30 + 28 * q^32 + 8 * q^33 + 14 * q^34 - 28 * q^35 - 72 * q^38 - 6 * q^40 - 12 * q^41 - 48 * q^42 - 24 * q^43 + 28 * q^44 - 50 * q^46 + 28 * q^49 + 12 * q^50 - 100 * q^51 + 24 * q^52 + 4 * q^54 + 10 * q^56 - 4 * q^57 - 84 * q^58 - 8 * q^59 + 16 * q^60 - 36 * q^62 + 48 * q^65 - 120 * q^66 - 12 * q^67 + 48 * q^68 - 26 * q^70 - 20 * q^74 - 40 * q^75 + 4 * q^76 - 48 * q^78 + 48 * q^80 - 32 * q^81 - 52 * q^82 - 4 * q^83 + 48 * q^84 - 62 * q^86 + 100 * q^88 - 28 * q^89 - 84 * q^90 - 36 * q^91 - 50 * q^92 + 40 * q^94 - 30 * q^96 + 4 * q^97 + 18 * q^98 + 96 * 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.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	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$