Space of modular forms of level 2176, weight 1, and Character 2176.co

• Label: 2176.1.co
• Level: $2176$
• Weight: $1$
• Character orbit: 2176.co
• Rep. character: $\chi_{2176}(65,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $32$
• Newform subspaces: $4$
• Sturm bound: $288$
• Trace bound: $53$

Defining parameters

Level:	\( N \)	\(=\)	\( 2176 = 2^{7} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2176.co (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 136 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(288\)
Trace bound:			\(53\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2176, [\chi])\).

	Total	New	Old
Modular forms	192	32	160
Cusp forms	64	32	32
Eisenstein series	128	0	128

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	32	0	0	0

Trace form

\( 32 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2176, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2176.1.co.a	$2176$	$1$	2176.co	136.q	$16$	$8$	$1$	$1.086$	\(\Q(\zeta_{16})\)	$D_{16}$	\(\Q(\sqrt{-2}) \)	None		✓			2176.1.co.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{16}^{2}-\zeta_{16}^{7})q^{3}+(-\zeta_{16}+\zeta_{16}^{4}+\cdots)q^{9}+\cdots\)
2176.1.co.b	$2176$	$1$	2176.co	136.q	$16$	$8$	$1$	$1.086$	\(\Q(\zeta_{16})\)	$D_{16}$	\(\Q(\sqrt{-1}) \)	None		✓			2176.1.co.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{16}^{2}+\zeta_{16}^{3})q^{5}+\zeta_{16}q^{9}+(\zeta_{16}^{5}+\cdots)q^{13}+\cdots\)
2176.1.co.c	$2176$	$1$	2176.co	136.q	$16$	$8$	$1$	$1.086$	\(\Q(\zeta_{16})\)	$D_{16}$	\(\Q(\sqrt{-1}) \)	None		✓			2176.1.co.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{16}^{2}-\zeta_{16}^{3})q^{5}+\zeta_{16}q^{9}+(-\zeta_{16}^{5}+\cdots)q^{13}+\cdots\)
2176.1.co.d	$2176$	$1$	2176.co	136.q	$16$	$8$	$1$	$1.086$	\(\Q(\zeta_{16})\)	$D_{16}$	\(\Q(\sqrt{-2}) \)	None		✓			2176.1.co.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{16}^{2}+\zeta_{16}^{7})q^{3}+(-\zeta_{16}+\zeta_{16}^{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2176, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2176, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(1088, [\chi])\)\(^{\oplus 2}\)