Space of modular forms of level 46, weight 3, and Character 46.d

• Label: 46.3.d
• Level: $46$
• Weight: $3$
• Character orbit: 46.d
• Rep. character: $\chi_{46}(5,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $40$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	46.d (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(18\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(46, [\chi])\).

	Total	New	Old
Modular forms	140	40	100
Cusp forms	100	40	60
Eisenstein series	40	0	40

Trace form

\( 40 q + 4 q^{3} - 8 q^{4} - 8 q^{6} + 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(46, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
46.3.d.a	$46$	$3$	46.d	23.d	$22$	$40$	$4$	$1.253$		None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$

Decomposition of \(S_{3}^{\mathrm{old}}(46, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(46, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)