Space of modular forms of level 35, weight 2, and Character 35.j

• Label: 35.2.j
• Level: $35$
• Weight: $2$
• Character orbit: 35.j
• Rep. character: $\chi_{35}(4,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	35.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(35, [\chi])\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	4	4	0
Eisenstein series	8	8	0

Trace form

4 * q - 2 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^9 - 4 * q^10 + 8 * q^14 + 8 * q^15 + 2 * q^16 + 12 * q^19 + 4 * q^20 - 10 * q^21 + 6 * q^24 + 6 * q^25 - 4 * q^26 - 28 * q^29 + 2 * q^30 - 4 * q^31 - 8 * q^34 - 16 * q^35 + 8 * q^36 - 4 * q^39 - 12 * q^40 + 20 * q^41 - 4 * q^45 + 6 * q^46 + 26 * q^49 + 16 * q^50 + 4 * q^51 + 10 * q^54 + 6 * q^56 + 20 * q^59 - 4 * q^60 - 14 * q^61 - 28 * q^64 + 8 * q^65 - 12 * q^69 - 10 * q^70 - 8 * q^71 - 16 * q^74 - 8 * q^75 - 24 * q^76 - 4 * q^79 + 2 * q^80 - 2 * q^81 + 8 * q^84 + 16 * q^85 - 14 * q^86 + 18 * q^89 + 16 * q^90 - 4 * q^91 + 12 * q^95 + 10 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(35, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.2.j.a	$35$	$2$	35.j	35.j	$6$	$4$	$2$	$0.279$	\(\Q(\zeta_{12})\)	None		✓	✓	✓	35.2.j.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)