Space of modular forms of level 1776, weight 1, and Character 1776.z

• Label: 1776.1.z
• Level: $1776$
• Weight: $1$
• Character orbit: 1776.z
• Rep. character: $\chi_{1776}(221,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $304$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1776 = 2^{4} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1776.z (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1776 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(304\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1776, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	24	24	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	16	0	8	0

Trace form

\( 24 q - 8 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1776, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1776.1.z.a	$1776$	$1$	1776.z	1776.z	$4$	$4$	$2$	$0.886$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}-q^{4}+(-1+\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
1776.1.z.b	$1776$	$1$	1776.z	1776.z	$4$	$4$	$2$	$0.886$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$		\(q-\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}-q^{4}+(1-\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
1776.1.z.c	$1776$	$1$	1776.z	1776.z	$4$	$16$	$8$	$0.886$	\(\Q(\zeta_{32})\)	$D_{16}$	\(\Q(\sqrt{-111}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{32}^{3}q^{2}+\zeta_{32}^{4}q^{3}+\zeta_{32}^{6}q^{4}+\cdots\)