Space of modular forms of level 4012, weight 2, and Character 4012.b

• Label: 4012.2.b
• Level: $4012$
• Weight: $2$
• Character orbit: 4012.b
• Rep. character: $\chi_{4012}(237,\cdot)$
• Character field: $\Q$
• Dimension: $86$
• Newform subspaces: $2$
• Sturm bound: $1080$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4012.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(1080\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4012, [\chi])\).

	Total	New	Old
Modular forms	546	86	460
Cusp forms	534	86	448
Eisenstein series	12	0	12

Trace form

\( 86 q - 90 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4012, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
4012.2.b.a	$4012$	$2$	4012.b	17.b	$2$	$40$	$40$	$32.036$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
4012.2.b.b	$4012$	$2$	4012.b	17.b	$2$	$46$	$46$	$32.036$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(4012, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4012, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1003, [\chi])\)\(^{\oplus 3}\)