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

• Label: 296.2.g
• Level: $296$
• Weight: $2$
• Character orbit: 296.g
• Rep. character: $\chi_{296}(73,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• 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.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
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	42	10	32
Cusp forms	34	10	24
Eisenstein series	8	0	8

Trace form

10 * q + 2 * q^3 - 4 * q^7 + 12 * q^9 + 2 * q^11 - 8 * q^21 + 4 * q^25 + 8 * q^27 + 4 * q^33 - 6 * q^37 - 26 * q^41 + 8 * q^47 + 14 * q^49 - 20 * q^53 - 12 * q^63 - 4 * q^65 - 2 * q^67 - 4 * q^71 - 14 * q^73 - 48 * q^75 + 18 * q^81 - 36 * q^83 + 8 * q^85 + 4 * q^95 - 28 * 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.g.a	$296$	$2$	296.g	37.b	$2$	$10$	$10$	$2.364$	10.0.\(\cdots\).1	None		✓	✓	✓	296.2.g.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(-4\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-\beta _{7}q^{5}-\beta _{3}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(296, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(296, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 2}\)