Space of modular forms of level 35, weight 8, and Character 35.f

• Label: 35.8.f
• Level: $35$
• Weight: $8$
• Character orbit: 35.f
• Rep. character: $\chi_{35}(13,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $52$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	35.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(35, [\chi])\).

	Total	New	Old
Modular forms	60	60	0
Cusp forms	52	52	0
Eisenstein series	8	8	0

Trace form

52 * q - 4 * q^2 + 1740 * q^7 + 2512 * q^8 + 140 * q^11 + 17360 * q^15 - 100216 * q^16 - 41368 * q^18 - 82116 * q^21 - 112004 * q^22 + 178232 * q^23 + 134000 * q^25 - 436688 * q^28 + 302420 * q^30 + 527472 * q^32 + 624140 * q^35 - 488968 * q^36 + 56376 * q^37 - 296780 * q^42 + 3019092 * q^43 - 761424 * q^46 - 8750140 * q^50 + 952708 * q^51 - 1602620 * q^53 + 2151896 * q^56 + 7200820 * q^57 + 1673732 * q^58 + 3143920 * q^60 - 10282560 * q^63 + 4745760 * q^65 - 3520004 * q^67 + 17232580 * q^70 - 20922360 * q^71 - 4287064 * q^72 - 18782404 * q^77 + 36427100 * q^78 - 18196580 * q^81 - 21543220 * q^85 - 27183144 * q^86 + 51543136 * q^88 + 48113204 * q^91 + 43427112 * q^92 - 40770940 * q^93 - 53342660 * q^95 - 55279908 * q^98

Decomposition of \(S_{8}^{\mathrm{new}}(35, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.8.f.a	$35$	$8$	35.f	35.f	$4$	$52$	$26$	$10.933$		None		✓	✓	✓	35.8.f.a	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(1740\)		$\mathrm{SU}(2)[C_{4}]$