Space of modular forms of level 3479, weight 1, and Character 3479.ex

• Label: 3479.1.ex
• Level: $3479$
• Weight: $1$
• Character orbit: 3479.ex
• Rep. character: $\chi_{3479}(67,\cdot)$
• Character field: $\Q(\zeta_{210})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $336$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3479 = 7^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3479.ex (of order \(210\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 497 \)
Character field:			\(\Q(\zeta_{210})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(336\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3479, [\chi])\).

	Total	New	Old
Modular forms	432	240	192
Cusp forms	48	48	0
Eisenstein series	384	192	192

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	48	0	0	0

Trace form

\( 48 q + 3 q^{2} + 2 q^{4} - 2 q^{8} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3479, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3479.1.ex.a	$3479$	$1$	3479.ex	497.ad	$210$	$48$	$1$	$1.736$	\(\Q(\zeta_{210})\)	$D_{70}$	\(\Q(\sqrt{-7}) \)	None		$8$	$0$	\(3\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{210}^{40}+\zeta_{210}^{52})q^{2}+(\zeta_{210}^{80}+\zeta_{210}^{92}+\cdots)q^{4}+\cdots\)