Space of modular forms of level 472, weight 2, and Character 472.l

• Label: 472.2.l
• Level: $472$
• Weight: $2$
• Character orbit: 472.l
• Rep. character: $\chi_{472}(11,\cdot)$
• Character field: $\Q(\zeta_{58})$
• Dimension: $1624$
• Newform subspaces: $2$
• Sturm bound: $120$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 472 = 2^{3} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	472.l (of order \(58\) and degree \(28\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 472 \)
Character field:			\(\Q(\zeta_{58})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(120\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(472, [\chi])\).

	Total	New	Old
Modular forms	1736	1736	0
Cusp forms	1624	1624	0
Eisenstein series	112	112	0

Trace form

\( 1624 q - 29 q^{2} - 54 q^{3} - 27 q^{4} - 29 q^{6} - 29 q^{8} - 108 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(472, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
472.2.l.a	$472$	$2$	472.l	472.l	$58$	$56$	$2$	$3.769$		\(\Q(\sqrt{-2}) \)		✓	472.2.l.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{58}]$
472.2.l.b	$472$	$2$	472.l	472.l	$58$	$1568$	$56$	$3.769$		None		✓	472.2.l.b	$4$	$0$	\(-29\)	\(-58\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{58}]$