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

• Label: 88.3.j
• Level: $88$
• Weight: $3$
• Character orbit: 88.j
• Rep. character: $\chi_{88}(17,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $24$
• 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.j (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{10})\)
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	112	24	88
Cusp forms	80	24	56
Eisenstein series	32	0	32

Trace form

24 * q + 4 * q^3 - 6 * q^9 - 10 * q^11 + 60 * q^15 + 40 * q^17 + 30 * q^19 + 32 * q^23 - 102 * q^25 - 122 * q^27 - 80 * q^29 - 64 * q^31 - 86 * q^33 - 240 * q^35 + 48 * q^37 - 240 * q^39 - 60 * q^41 - 112 * q^45 + 180 * q^47 + 350 * q^49 + 550 * q^51 + 132 * q^53 + 388 * q^55 + 530 * q^57 - 26 * q^59 + 80 * q^61 + 80 * q^63 + 212 * q^67 - 252 * q^69 - 540 * q^71 - 580 * q^73 - 106 * q^75 - 540 * q^77 - 280 * q^79 - 228 * q^81 - 90 * q^83 - 120 * q^85 - 324 * q^89 + 228 * q^91 + 988 * q^93 + 280 * q^95 + 410 * q^97 + 318 * 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.j.a	$88$	$3$	88.j	11.d	$10$	$24$	$6$	$2.398$		None		✓	✓	✓	88.3.j.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

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