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

• Label: 2016.1.f
• Level: $2016$
• Weight: $1$
• Character orbit: 2016.f
• Rep. character: $\chi_{2016}(1441,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $384$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2016.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(384\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	44	4	40
Cusp forms	12	4	8
Eisenstein series	32	0	32

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

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

Trace form

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

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.f.a	$2016$	$1$	2016.f	7.b	$2$	$4$	$4$	$1.006$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-21}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$		\(q+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(2016, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)