Space of modular forms of level 88, weight 3, and Character 88.h

• Label: 88.3.h
• Level: $88$
• Weight: $3$
• Character orbit: 88.h
• Rep. character: $\chi_{88}(65,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$88 = 2^{3} \cdot 11$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	88.h (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$11$
Character field:			$\Q$
Newform subspaces:			$1$
Sturm bound:			$36$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{3}(88, [\chi])$.

	Total	New	Old
Modular forms	28	6	22
Cusp forms	20	6	14
Eisenstein series	8	0	8

Trace form

6 * q - 4 * q^3 + 6 * q^9 + 10 * q^11 - 52 * q^23 + 22 * q^25 + 32 * q^27 - 36 * q^31 - 64 * q^33 - 48 * q^37 + 172 * q^45 - 60 * q^47 - 170 * q^49 + 108 * q^53 + 172 * q^55 + 236 * q^59 - 292 * q^67 + 92 * q^69 + 300 * q^71 - 244 * q^75 - 240 * q^77 - 362 * q^81 + 384 * q^89 - 48 * q^91 - 148 * q^93 + 400 * q^97 + 182 * q^99

Decomposition of $S_{3}^{\mathrm{new}}(88, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
88.3.h.a	$88$	$3$	88.h	11.b	$2$	$6$	$6$	$2.398$	6.0.1750426112.2	None		✓	✓	✓	88.3.h.a	$2$	$0$	$0$	$-4$	$0$	$0$	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{1})q^{3}+\beta _{3}q^{5}-\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots$

Decomposition of $S_{3}^{\mathrm{old}}(88, [\chi])$ into lower level spaces

$S_{3}^{\mathrm{old}}(88, [\chi]) \simeq$ $S_{3}^{\mathrm{new}}(11, [\chi])$$^{\oplus 4}$$\oplus$$S_{3}^{\mathrm{new}}(22, [\chi])$$^{\oplus 3}$$\oplus$$S_{3}^{\mathrm{new}}(44, [\chi])$$^{\oplus 2}$