Space of modular forms of level 35, weight 5, and Character 35.g

• Label: 35.5.g
• Level: $35$
• Weight: $5$
• Character orbit: 35.g
• Rep. character: $\chi_{35}(8,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(20\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(35, [\chi])\).

	Total	New	Old
Modular forms	36	24	12
Cusp forms	28	24	4
Eisenstein series	8	0	8

Trace form

\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(35, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.5.g.a	$35$	$5$	35.g	5.c	$4$	$24$	$12$	$3.618$		None		$2$	$0$	\(0\)	\(20\)	\(-48\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{5}^{\mathrm{old}}(35, [\chi])\) into lower level spaces

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