Space of modular forms of level 1472, weight 1, and Character 1472.s

• Label: 1472.1.s
• Level: $1472$
• Weight: $1$
• Character orbit: 1472.s
• Rep. character: $\chi_{1472}(45,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1472 = 2^{6} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1472.s (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1472 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1472, [\chi])\).

	Total	New	Old
Modular forms	40	40	0
Cusp forms	24	24	0
Eisenstein series	16	16	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q + 24 q^{58} + 24 q^{72} - 24 q^{78}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1472, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1472.1.s.a	$1472$	$1$	1472.s	1472.s	$16$	$8$	$1$	$0.735$	\(\Q(\zeta_{16})\)	$D_{16}$	\(\Q(\sqrt{-23}) \)	None		✓			1472.1.s.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{16}q^{2}+(\zeta_{16}-\zeta_{16}^{4})q^{3}+\zeta_{16}^{2}q^{4}+\cdots\)
1472.1.s.b	$1472$	$1$	1472.s	1472.s	$16$	$16$	$2$	$0.735$	\(\Q(\zeta_{48})\)	$D_{48}$	\(\Q(\sqrt{-23}) \)	None		✓	✓		1472.1.s.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{48}q^{2}+(-\zeta_{48}^{4}+\zeta_{48}^{17})q^{3}+\cdots\)