Space of modular forms of level 1001, weight 2, and Character 1001.d

• Label: 1001.2.d
• Level: $1001$
• Weight: $2$
• Character orbit: 1001.d
• Rep. character: $\chi_{1001}(155,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $224$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(224\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1001, [\chi])\).

	Total	New	Old
Modular forms	116	72	44
Cusp forms	108	72	36
Eisenstein series	8	0	8

Trace form

\( 72 q - 76 q^{4} + 80 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1001, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1001.2.d.a	$1001$	$2$	1001.d	13.b	$2$	$2$	$2$	$7.993$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-2q^{3}+q^{4}-2iq^{5}-2iq^{6}+\cdots\)
1001.2.d.b	$1001$	$2$	1001.d	13.b	$2$	$30$	$30$	$7.993$		None		$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1001.2.d.c	$1001$	$2$	1001.d	13.b	$2$	$40$	$40$	$7.993$		None		$2$	$0$	\(0\)	\(12\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1001, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1001, [\chi]) \cong \)