Space of modular forms of level 469, weight 1, and Character 469.bl

• Label: 469.1.bl
• Level: $469$
• Weight: $1$
• Character orbit: 469.bl
• Rep. character: $\chi_{469}(6,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $45$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 469 = 7 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	469.bl (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 469 \)
Character field:			\(\Q(\zeta_{66})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(45\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(469, [\chi])\).

	Total	New	Old
Modular forms	60	60	0
Cusp forms	20	20	0
Eisenstein series	40	40	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	20	0	0	0

Trace form

\( 20 q + 2 q^{2} + 3 q^{4} + q^{7} - 8 q^{8} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(469, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
469.1.bl.a	$469$	$1$	469.bl	469.al	$66$	$20$	$1$	$0.234$	\(\Q(\zeta_{33})\)	$D_{33}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(1\)	$1$		\(q+(\zeta_{66}^{10}+\zeta_{66}^{16})q^{2}+(\zeta_{66}^{20}+\zeta_{66}^{26}+\cdots)q^{4}+\cdots\)