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

• Label: 471.2.b
• Level: $471$
• Weight: $2$
• Character orbit: 471.b
• Rep. character: $\chi_{471}(313,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $2$
• Sturm bound: $105$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 157 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
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	54	26	28
Cusp forms	50	26	24
Eisenstein series	4	0	4

Trace form

\( 26 q + 2 q^{3} - 26 q^{4} + 26 q^{9} + O(q^{10}) \)

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.b.a	$471$	$2$	471.b	157.b	$2$	$12$	$12$	$3.761$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-12\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
471.2.b.b	$471$	$2$	471.b	157.b	$2$	$14$	$14$	$3.761$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(14\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)

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

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