Space of modular forms of level 408, weight 1, and Character 408.bg

• Label: 408.1.bg
• Level: $408$
• Weight: $1$
• Character orbit: 408.bg
• Rep. character: $\chi_{408}(11,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $72$
• Trace bound: $12$

Defining parameters

Level:	\( N \)	\(=\)	\( 408 = 2^{3} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	408.bg (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 408 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(72\)
Trace bound:			\(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(408, [\chi])\).

	Total	New	Old
Modular forms	48	48	0
Cusp forms	16	16	0
Eisenstein series	32	32	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(408, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
408.1.bg.a	$408$	$1$	408.bg	408.ag	$16$	$8$	$1$	$0.204$	\(\Q(\zeta_{16})\)	$D_{16}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{16}q^{2}+\zeta_{16}^{6}q^{3}+\zeta_{16}^{2}q^{4}-\zeta_{16}^{7}q^{6}+\cdots\)
408.1.bg.b	$408$	$1$	408.bg	408.ag	$16$	$8$	$1$	$0.204$	\(\Q(\zeta_{16})\)	$D_{16}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{16}q^{2}+\zeta_{16}^{5}q^{3}+\zeta_{16}^{2}q^{4}+\zeta_{16}^{6}q^{6}+\cdots\)