Space of modular forms of level 471, weight 2, and Character 471.e

• Label: 471.2.e
• Level: $471$
• Weight: $2$
• Character orbit: 471.e
• Rep. character: $\chi_{471}(169,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $54$
• Newform subspaces: $3$
• Sturm bound: $105$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 157 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(105\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(471, [\chi])\).

	Total	New	Old
Modular forms	110	54	56
Cusp forms	102	54	48
Eisenstein series	8	0	8

Trace form

\( 54 q + 4 q^{2} - q^{3} + 56 q^{4} - 6 q^{5} - 27 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(471, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
471.2.e.a	$471$	$2$	471.e	157.c	$3$	$4$	$2$	$3.761$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{3}q^{2}+(1+\beta _{2})q^{3}-2\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots\)
471.2.e.b	$471$	$2$	471.e	157.c	$3$	$22$	$11$	$3.761$		None		$2$	$0$	\(2\)	\(11\)	\(-4\)	\(4\)		$\mathrm{SU}(2)[C_{3}]$
471.2.e.c	$471$	$2$	471.e	157.c	$3$	$28$	$14$	$3.761$		None		$2$	$0$	\(2\)	\(-14\)	\(-2\)	\(4\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(471, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(471, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(157, [\chi])\)\(^{\oplus 2}\)