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

• Label: 35.5.c
• Level: $35$
• Weight: $5$
• Character orbit: 35.c
• Rep. character: $\chi_{35}(34,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $5$
• Sturm bound: $20$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(20\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

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

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

Trace form

\( 14 q - 100 q^{4} + 264 q^{9} + O(q^{10}) \)

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.c.a	$35$	$5$	35.c	35.c	$2$	$1$	$1$	$3.618$	\(\Q\)	\(\Q(\sqrt{-35}) \)	✓	$2$	$0$	\(0\)	\(-17\)	\(25\)	\(49\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-17q^{3}+2^{4}q^{4}+5^{2}q^{5}+7^{2}q^{7}+\cdots\)
35.5.c.b	$35$	$5$	35.c	35.c	$2$	$1$	$1$	$3.618$	\(\Q\)	\(\Q(\sqrt{-35}) \)	✓	$2$	$0$	\(0\)	\(17\)	\(-25\)	\(-49\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+17q^{3}+2^{4}q^{4}-5^{2}q^{5}-7^{2}q^{7}+\cdots\)
35.5.c.c	$35$	$5$	35.c	35.c	$2$	$2$	$2$	$3.618$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(-10\)	\(-10\)	\(-70\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-5q^{3}+10q^{4}+(-5+10\beta )q^{5}+\cdots\)
35.5.c.d	$35$	$5$	35.c	35.c	$2$	$2$	$2$	$3.618$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(10\)	\(10\)	\(70\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+5q^{3}+10q^{4}+(5-10\beta )q^{5}+\cdots\)
35.5.c.e	$35$	$5$	35.c	35.c	$2$	$8$	$8$	$3.618$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+3\beta _{3}q^{3}+(-22+\beta _{2})q^{4}+\cdots\)