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

• Label: 35.3.d
• Level: $35$
• Weight: $3$
• Character orbit: 35.d
• Rep. character: $\chi_{35}(6,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $12$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(12\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(35, [\chi])\).

	Total	New	Old
Modular forms	10	4	6
Cusp forms	6	4	2
Eisenstein series	4	0	4

Trace form

\( 4 q + 2 q^{2} - 6 q^{4} + 10 q^{7} - 2 q^{8} - 14 q^{9} + O(q^{10}) \)

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.d.a	$35$	$3$	35.d	7.b	$2$	$2$	$2$	$0.954$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(14\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+2\beta q^{3}-3q^{4}+\beta q^{5}-2\beta q^{6}+\cdots\)
35.3.d.b	$35$	$3$	35.d	7.b	$2$	$2$	$2$	$0.954$	\(\Q(\sqrt{-5}) \)	None		$2$	$0$	\(4\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{2}+\beta q^{3}-\beta q^{5}+2\beta q^{6}+(-2+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(35, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(35, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)