Space of modular forms of level 35, weight 3, and Character 35.h

• Label: 35.3.h
• Level: $35$
• Weight: $3$
• Character orbit: 35.h
• Rep. character: $\chi_{35}(26,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(35, [\chi])\).

	Total	New	Old
Modular forms	20	12	8
Cusp forms	12	12	0
Eisenstein series	8	0	8

Trace form

12 * q - 2 * q^2 - 6 * q^3 - 10 * q^4 - 2 * q^7 - 4 * q^8 + 14 * q^9 - 14 * q^11 + 18 * q^12 - 2 * q^14 - 20 * q^15 - 22 * q^16 + 48 * q^17 + 64 * q^18 - 30 * q^19 - 84 * q^21 - 88 * q^22 - 14 * q^23 - 36 * q^24 + 30 * q^25 + 66 * q^26 + 202 * q^28 + 64 * q^29 + 20 * q^30 + 132 * q^31 - 54 * q^32 - 192 * q^33 + 30 * q^35 + 156 * q^36 + 44 * q^37 - 300 * q^38 - 24 * q^39 - 138 * q^42 - 4 * q^43 + 6 * q^44 - 180 * q^45 - 214 * q^46 + 204 * q^47 - 24 * q^49 - 20 * q^50 - 132 * q^51 + 252 * q^52 + 196 * q^53 + 168 * q^54 - 460 * q^56 - 48 * q^57 + 158 * q^58 + 72 * q^59 + 150 * q^60 + 72 * q^61 + 536 * q^63 - 140 * q^64 + 30 * q^65 + 744 * q^66 - 138 * q^67 - 348 * q^68 + 240 * q^70 - 8 * q^71 - 196 * q^72 - 528 * q^73 + 50 * q^74 - 30 * q^75 - 176 * q^77 - 312 * q^78 - 12 * q^79 - 240 * q^80 - 310 * q^81 - 378 * q^82 - 276 * q^84 - 40 * q^86 + 138 * q^87 + 604 * q^88 + 204 * q^89 - 480 * q^91 + 732 * q^92 + 84 * q^93 - 42 * q^94 + 60 * q^95 + 540 * q^96 + 898 * q^98 - 44 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(35, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.3.h.a	$35$	$3$	35.h	7.d	$6$	$12$	$6$	$0.954$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓	✓	35.3.h.a	$2$	$0$	\(-2\)	\(-6\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{7})q^{3}+(-2+\cdots)q^{4}+\cdots\)