Space of modular forms of level 1002, weight 2, and Character 1002.d

• Label: 1002.2.d
• Level: $1002$
• Weight: $2$
• Character orbit: 1002.d
• Rep. character: $\chi_{1002}(1001,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $1$
• Sturm bound: $336$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1002 = 2 \cdot 3 \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1002.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 501 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(336\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1002, [\chi])\).

	Total	New	Old
Modular forms	172	56	116
Cusp forms	164	56	108
Eisenstein series	8	0	8

Trace form

\( 56 q - 56 q^{4} + 4 q^{6} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1002, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1002.2.d.a	$1002$	$2$	1002.d	501.c	$2$	$56$	$56$	$8.001$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1002, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1002, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(501, [\chi])\)\(^{\oplus 2}\)