Space of modular forms of level 1003, weight 2, and Character 1003.d

• Label: 1003.2.d
• Level: $1003$
• Weight: $2$
• Character orbit: 1003.d
• Rep. character: $\chi_{1003}(237,\cdot)$
• Character field: $\Q$
• Dimension: $88$
• Newform subspaces: $4$
• Sturm bound: $180$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(180\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1003, [\chi])\).

	Total	New	Old
Modular forms	92	88	4
Cusp forms	88	88	0
Eisenstein series	4	0	4

Trace form

\( 88 q - 2 q^{2} + 82 q^{4} - 6 q^{8} - 100 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1003, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1003.2.d.a	$1003$	$2$	1003.d	17.b	$2$	$2$	$2$	$8.009$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-q^{4}-3q^{8}+3q^{9}-\beta q^{11}+\cdots\)
1003.2.d.b	$1003$	$2$	1003.d	17.b	$2$	$4$	$4$	$8.009$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-2\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
1003.2.d.c	$1003$	$2$	1003.d	17.b	$2$	$38$	$38$	$8.009$		None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1003.2.d.d	$1003$	$2$	1003.d	17.b	$2$	$44$	$44$	$8.009$		None		$2$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$