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 + 2 * q^10 + 14 * q^12 + 2 * q^14 + 8 * q^15 - 12 * q^16 - 6 * q^18 - 8 * q^20 + 10 * q^22 - 12 * q^23 - 8 * q^24 - 36 * q^25 - 14 * q^26 + 8 * q^28 + 20 * q^30 - 4 * q^31 - 20 * q^32 + 8 * q^33 - 24 * q^34 + 22 * q^36 - 16 * q^38 + 8 * q^39 - 6 * q^40 - 8 * q^41 - 34 * q^42 + 30 * q^44 + 38 * q^46 - 24 * q^47 + 10 * q^48 + 36 * q^49 + 4 * q^50 + 36 * q^52 - 6 * q^54 + 16 * q^55 - 16 * q^56 - 8 * q^57 + 10 * q^58 - 40 * q^60 + 6 * q^62 - 4 * q^64 + 26 * q^66 - 16 * q^68 + 48 * q^70 + 32 * q^71 - 24 * q^72 + 48 * q^76 + 10 * q^78 + 36 * q^79 + 28 * q^81 - 34 * q^82 + 40 * q^84 - 28 * q^86 - 48 * q^87 - 8 * q^88 + 16 * q^89 + 40 * q^90 - 32 * q^92 + 6 * q^94 - 16 * q^95 + 40 * q^96 + 16 * q^97 - 30 * q^98

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	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{2}]$