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

• Label: 35.3.l
• Level: $35$
• Weight: $3$
• Character orbit: 35.l
• Rep. character: $\chi_{35}(2,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.l (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{12})\)
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	40	40	0
Cusp forms	24	24	0
Eisenstein series	16	16	0

Trace form

\( 24 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 6 q^{7} - 36 q^{8} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.3.l.a	$35$	$3$	35.l	35.l	$12$	$24$	$6$	$0.954$		None		$4$	$0$	\(-2\)	\(-2\)	\(-4\)	\(-6\)		$\mathrm{SU}(2)[C_{12}]$