Space of modular forms of level 1035, weight 1, and Character 1035.d

• Label: 1035.1.d
• Level: $1035$
• Weight: $1$
• Character orbit: 1035.d
• Rep. character: $\chi_{1035}(919,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $144$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1035.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(144\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1035, [\chi])\).

	Total	New	Old
Modular forms	10	4	6
Cusp forms	2	2	0
Eisenstein series	8	2	6

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + 2 q^{4} + 2 q^{16} + 2 q^{25} - 4 q^{31} - 2 q^{49} + 2 q^{64} - 4 q^{85}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1035, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1035.1.d.a	$1035$	$1$	1035.d	115.c	$2$	$1$	$1$	$0.517$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-115}) \)	\(\Q(\sqrt{69}) \)	✓	✓			1035.1.d.a	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+q^{4}-q^{5}+q^{16}+2q^{17}-q^{20}+\cdots\)
1035.1.d.b	$1035$	$1$	1035.d	115.c	$2$	$1$	$1$	$0.517$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-115}) \)	\(\Q(\sqrt{69}) \)	✓	✓			1035.1.d.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+q^{4}+q^{5}+q^{16}-2q^{17}+q^{20}+\cdots\)