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

• Label: 35.6.b
• Level: $35$
• Weight: $6$
• Character orbit: 35.b
• Rep. character: $\chi_{35}(29,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	22	14	8
Cusp forms	18	14	4
Eisenstein series	4	0	4

Trace form

\( 14 q - 212 q^{4} + 156 q^{5} - 180 q^{6} - 796 q^{9} + O(q^{10}) \)

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.b.a	$35$	$6$	35.b	5.b	$2$	$14$	$14$	$5.613$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓	✓	✓	35.6.b.a	$2$	$0$	\(0\)	\(0\)	\(156\)	\(0\)	$2^{4}\cdot 5^{3}\cdot 7^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+\beta _{6}q^{3}+(-15+\beta _{1})q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(35, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(35, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)