Space of modular forms of level 75, weight 8, and Character 75.l

• Label: 75.8.l
• Level: $75$
• Weight: $8$
• Character orbit: 75.l
• Rep. character: $\chi_{75}(2,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $544$
• Newform subspaces: $1$
• Sturm bound: $80$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	75.l (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 75 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(80\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(75, [\chi])\).

	Total	New	Old
Modular forms	576	576	0
Cusp forms	544	544	0
Eisenstein series	32	32	0

Trace form

544 * q - 34 * q^3 - 20 * q^4 - 6 * q^6 - 1364 * q^7 - 10 * q^9 + 3160 * q^10 + 2018 * q^12 - 16868 * q^13 - 37570 * q^15 + 507892 * q^16 + 106550 * q^18 + 70800 * q^19 - 6 * q^21 - 195160 * q^22 - 444200 * q^25 + 264158 * q^27 + 692032 * q^28 - 892390 * q^30 - 12 * q^31 + 877790 * q^33 - 1828180 * q^34 - 65542 * q^36 + 635596 * q^37 - 3868770 * q^39 + 1574020 * q^40 + 4577310 * q^42 - 1397348 * q^43 + 3411430 * q^45 - 12 * q^46 - 12135404 * q^48 - 16 * q^51 + 6428876 * q^52 + 16485420 * q^54 - 2324900 * q^55 + 4119286 * q^57 - 986360 * q^58 - 25245250 * q^60 - 12 * q^61 + 6259012 * q^63 + 363500 * q^64 - 1119750 * q^66 + 3427476 * q^67 - 12994880 * q^69 + 9814160 * q^70 - 611970 * q^72 + 10236732 * q^73 + 19853790 * q^75 - 131104 * q^76 + 24801340 * q^78 - 8474460 * q^79 + 10854734 * q^81 + 44639220 * q^82 - 52907530 * q^84 - 82807380 * q^85 - 15442020 * q^87 + 33548360 * q^88 - 11540050 * q^90 - 12 * q^91 + 14982652 * q^93 + 60673460 * q^94 + 1218042 * q^96 - 22089384 * q^97

Decomposition of \(S_{8}^{\mathrm{new}}(75, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
75.8.l.a	$75$	$8$	75.l	75.l	$20$	$544$	$68$	$23.429$		None		✓	✓	✓	75.8.l.a	$4$	$0$	\(0\)	\(-34\)	\(0\)	\(-1364\)		$\mathrm{SU}(2)[C_{20}]$