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

• Label: 35.2.f
• Level: $35$
• Weight: $2$
• Character orbit: 35.f
• Rep. character: $\chi_{35}(13,\cdot)$
• Character field: $\Q(\zeta_{4})$
• 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.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
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

\( 4 q - 4 q^{2} + 4 q^{7} - 8 q^{8} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.2.f.a	$35$	$2$	35.f	35.f	$4$	$4$	$2$	$0.279$	\(\Q(i, \sqrt{10})\)	None		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots\)