Space of modular forms of level 35, weight 6, and Character 35.f

• Label: 35.6.f
• Level: $35$
• Weight: $6$
• Character orbit: 35.f
• Rep. character: $\chi_{35}(13,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $36$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(35, [\chi])\).

	Total	New	Old
Modular forms	44	44	0
Cusp forms	36	36	0
Eisenstein series	8	8	0

Trace form

36 * q - 4 * q^2 - 196 * q^7 - 368 * q^8 + 412 * q^11 + 2960 * q^15 - 7672 * q^16 + 3368 * q^18 - 84 * q^21 + 4604 * q^22 + 2008 * q^23 - 7000 * q^25 + 21280 * q^28 - 5260 * q^30 - 6960 * q^32 - 34860 * q^35 + 9848 * q^36 + 7696 * q^37 + 58660 * q^42 - 50252 * q^43 - 8848 * q^46 + 74180 * q^50 - 49868 * q^51 - 85676 * q^53 - 155848 * q^56 - 84020 * q^57 + 226692 * q^58 + 306160 * q^60 + 88032 * q^63 - 157640 * q^65 - 185604 * q^67 - 183820 * q^70 + 12712 * q^71 + 19784 * q^72 + 219716 * q^77 - 200740 * q^78 + 498268 * q^81 + 78860 * q^85 + 22552 * q^86 - 895072 * q^88 - 242284 * q^91 + 517160 * q^92 + 643580 * q^93 + 573820 * q^95 + 413868 * q^98

Decomposition of \(S_{6}^{\mathrm{new}}(35, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.6.f.a	$35$	$6$	35.f	35.f	$4$	$36$	$18$	$5.613$		None		✓	✓	✓	35.6.f.a	$4$	$0$	\(-4\)	\(0\)	\(0\)	\(-196\)		$\mathrm{SU}(2)[C_{4}]$