Space of modular forms of level 504, weight 1, and Character 504.bn

• Label: 504.1.bn
• Level: $504$
• Weight: $1$
• Character orbit: 504.bn
• Rep. character: $\chi_{504}(13,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	504.bn (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 504 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(504, [\chi])\).

	Total	New	Old
Modular forms	16	16	0
Cusp forms	8	8	0
Eisenstein series	8	8	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q - 4 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(504, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
504.1.bn.a	$504$	$1$	504.bn	504.an	$6$	$2$	$1$	$0.252$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-14}) \)	None		$4$	$0$	\(-1\)	\(-2\)	\(-1\)	\(-1\)	$1$		\(q+\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{6}+\cdots\)
504.1.bn.b	$504$	$1$	504.bn	504.an	$6$	$2$	$1$	$0.252$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-14}) \)	None		$4$	$0$	\(-1\)	\(2\)	\(1\)	\(-1\)	$1$		\(q+\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{6}+\cdots\)
504.1.bn.c	$504$	$1$	504.bn	504.an	$6$	$4$	$2$	$0.252$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-14}) \)	None		$8$	$0$	\(2\)	\(0\)	\(0\)	\(2\)	$1$		\(q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{4}+\cdots\)