Space of modular forms of level 1005, weight 2, and Character 1005.g

• Label: 1005.2.g
• Level: $1005$
• Weight: $2$
• Character orbit: 1005.g
• Rep. character: $\chi_{1005}(401,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $2$
• Sturm bound: $272$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1005 = 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1005.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 201 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(272\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1005, [\chi])\).

	Total	New	Old
Modular forms	140	92	48
Cusp forms	132	92	40
Eisenstein series	8	0	8

Trace form

\( 92 q + 96 q^{4} + 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1005, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1005.2.g.a	$1005$	$2$	1005.g	201.d	$2$	$46$	$46$	$8.025$		None		$2$	$0$	\(0\)	\(0\)	\(-46\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1005.2.g.b	$1005$	$2$	1005.g	201.d	$2$	$46$	$46$	$8.025$		None		$2$	$0$	\(0\)	\(0\)	\(46\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1005, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1005, [\chi]) \cong \)