Space of modular forms of level 2016, weight 1, and Character 2016.bv

• Label: 2016.1.bv
• Level: $2016$
• Weight: $1$
• Character orbit: 2016.bv
• Rep. character: $\chi_{2016}(1105,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $384$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2016.bv (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 504 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(384\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2016, [\chi])\).

	Total	New	Old
Modular forms	64	16	48
Cusp forms	32	8	24
Eisenstein series	32	8	24

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

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

Decomposition of \(S_{1}^{\mathrm{new}}(2016, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2016.1.bv.a	$2016$	$1$	2016.bv	504.an	$6$	$2$	$1$	$1.006$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-14}) \)	None		$4$	$0$	\(0\)	\(-2\)	\(1\)	\(1\)	$1$		\(q-q^{3}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+q^{9}+\zeta_{6}^{2}q^{13}+\cdots\)
2016.1.bv.b	$2016$	$1$	2016.bv	504.an	$6$	$2$	$1$	$1.006$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-14}) \)	None		$4$	$0$	\(0\)	\(2\)	\(-1\)	\(1\)	$1$		\(q+q^{3}+\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+q^{9}-\zeta_{6}^{2}q^{13}+\cdots\)
2016.1.bv.c	$2016$	$1$	2016.bv	504.an	$6$	$4$	$2$	$1.006$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-14}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-\zeta_{12}^{3}q^{3}+(-\zeta_{12}-\zeta_{12}^{3})q^{5}+\zeta_{12}^{4}q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2016, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2016, [\chi]) \cong \)