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

• Label: 35.2.b
• Level: $35$
• Weight: $2$
• Character orbit: 35.b
• Rep. character: $\chi_{35}(29,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	35.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
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	6	2	4
Cusp forms	2	2	0
Eisenstein series	4	0	4

Trace form

2 * q - 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^9 + 4 * q^10 - 6 * q^11 + 4 * q^14 - 2 * q^15 - 8 * q^16 + 8 * q^20 - 2 * q^21 + 6 * q^25 + 4 * q^26 + 10 * q^29 - 8 * q^30 + 4 * q^31 - 28 * q^34 - 2 * q^35 - 8 * q^36 - 2 * q^39 + 4 * q^41 + 12 * q^44 - 8 * q^45 + 24 * q^46 - 2 * q^49 - 16 * q^50 + 14 * q^51 + 20 * q^54 + 12 * q^55 - 20 * q^59 + 4 * q^60 - 16 * q^61 + 16 * q^64 - 2 * q^65 - 12 * q^66 - 12 * q^69 - 8 * q^70 - 16 * q^71 - 8 * q^74 + 8 * q^75 + 10 * q^79 + 16 * q^80 + 2 * q^81 + 4 * q^84 + 14 * q^85 - 16 * q^86 + 8 * q^90 - 2 * q^91 + 12 * q^94 - 16 * q^96 - 12 * q^99

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.b.a	$35$	$2$	35.b	5.b	$2$	$2$	$2$	$0.279$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	35.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-i q^{3}-2 q^{4}+(-i-2)q^{5}+\cdots\)