Space of modular forms of level 88, weight 2, and Character 88.g

• Label: 88.2.g
• Level: $88$
• Weight: $2$
• Character orbit: 88.g
• Rep. character: $\chi_{88}(43,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	88.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 88 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(88, [\chi])\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	10	10	0
Eisenstein series	4	4	0

Trace form

10 * q - 4 * q^3 - 4 * q^4 + 2 * q^9 + 2 * q^11 - 8 * q^14 - 16 * q^16 + 12 * q^22 - 6 * q^25 + 24 * q^26 - 16 * q^27 - 4 * q^33 + 8 * q^34 - 20 * q^36 + 16 * q^38 - 24 * q^42 + 20 * q^44 + 40 * q^48 - 6 * q^49 - 16 * q^56 + 16 * q^58 - 20 * q^59 + 56 * q^60 - 16 * q^64 - 32 * q^66 + 36 * q^67 - 56 * q^70 + 36 * q^75 - 40 * q^78 + 56 * q^80 - 30 * q^81 - 40 * q^82 + 40 * q^86 - 24 * q^88 - 4 * q^89 + 32 * q^91 - 56 * q^92 + 12 * q^97 - 38 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(88, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
88.2.g.a	$88$	$2$	88.g	88.g	$2$	$2$	$2$	$0.703$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		✓			88.2.g.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{2}+2q^{3}-2q^{4}+2\beta q^{6}-2\beta q^{8}+\cdots\)
88.2.g.b	$88$	$2$	88.g	88.g	$2$	$8$	$8$	$0.703$	8.0.\(\cdots\).6	None		✓	✓		88.2.g.b	$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+(-1-\beta _{4})q^{3}+(-\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)