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

• Label: 3479.1.g
• Level: $3479$
• Weight: $1$
• Character orbit: 3479.g
• Rep. character: $\chi_{3479}(851,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $58$
• Newform subspaces: $7$
• Sturm bound: $336$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 3479 = 7^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3479.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 497 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(336\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	82	66	16
Cusp forms	66	58	8
Eisenstein series	16	8	8

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	54	4	0	0

Trace form

\( 58 q - 2 q^{3} - 25 q^{4} + 2 q^{5} + 4 q^{6} - 12 q^{8} - 25 q^{9} + O(q^{10}) \)

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.g.a	$3479$	$1$	3479.g	497.g	$6$	$2$	$1$	$1.736$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-71}) \)	\(\Q(\sqrt{497}) \)		$8$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{2}-3\zeta_{6}q^{4}-2q^{8}-\zeta_{6}^{2}q^{9}+\cdots\)
3479.1.g.b	$3479$	$1$	3479.g	497.g	$6$	$4$	$2$	$1.736$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		$4$	$0$	\(-2\)	\(-2\)	\(2\)	\(0\)	$1$		\(q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{5}+\cdots\)
3479.1.g.c	$3479$	$1$	3479.g	497.g	$6$	$4$	$2$	$1.736$	\(\Q(\sqrt{2}, \sqrt{-3})\)	$D_{4}$	\(\Q(\sqrt{-71}) \)	None		$8$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(2+2\beta _{2})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+3\beta _{2}q^{4}+\cdots\)
3479.1.g.d	$3479$	$1$	3479.g	497.g	$6$	$6$	$3$	$1.736$	6.0.64827.1	$D_{7}$	\(\Q(\sqrt{-71}) \)	None		$4$	$0$	\(1\)	\(-1\)	\(-1\)	\(0\)	$1$		\(q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5})q^{3}+\cdots\)
3479.1.g.e	$3479$	$1$	3479.g	497.g	$6$	$6$	$3$	$1.736$	6.0.64827.1	$D_{7}$	\(\Q(\sqrt{-71}) \)	None		$4$	$0$	\(1\)	\(1\)	\(1\)	\(0\)	$1$		\(q+\beta _{4}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots\)
3479.1.g.f	$3479$	$1$	3479.g	497.g	$6$	$12$	$6$	$1.736$	12.0.\(\cdots\).2	$D_{14}$	\(\Q(\sqrt{-71}) \)	None		$8$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\beta _{5}q^{2}+\beta _{9}q^{3}+(-\beta _{2}+\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots\)
3479.1.g.g	$3479$	$1$	3479.g	497.g	$6$	$24$	$12$	$1.736$	24.0.\(\cdots\).7	$D_{28}$	\(\Q(\sqrt{-71}) \)	None		$8$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\beta _{4}+\beta _{5}-\beta _{11}+\beta _{12})q^{2}-\beta _{6}q^{3}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3479, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3479, [\chi]) \cong \)