Space of modular forms of level 471, weight 1, and Character 471.n

• Label: 471.1.n
• Level: $471$
• Weight: $1$
• Character orbit: 471.n
• Rep. character: $\chi_{471}(56,\cdot)$
• Character field: $\Q(\zeta_{26})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $52$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	471.n (of order \(26\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 471 \)
Character field:			\(\Q(\zeta_{26})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(52\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(471, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	12	12	0
Eisenstein series	24	24	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q - q^{3} + q^{4} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(471, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
471.1.n.a	$471$	$1$	471.n	471.n	$26$	$12$	$1$	$0.235$	\(\Q(\zeta_{26})\)	$D_{26}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{26}^{2}q^{3}+\zeta_{26}^{11}q^{4}+(\zeta_{26}^{5}+\zeta_{26}^{12}+\cdots)q^{7}+\cdots\)