Space of modular forms of level 552, weight 1, and Character 552.h

• Label: 552.1.h
• Level: $552$
• Weight: $1$
• Character orbit: 552.h
• Rep. character: $\chi_{552}(275,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $4$
• Sturm bound: $96$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	552.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 552 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(552, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	6	6	0
Eisenstein series	4	4	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q - 3 q^{6} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(552, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
552.1.h.a	$552$	$1$	552.h	552.h	$2$	$1$	$1$	$0.275$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-138}) \)	\(\Q(\sqrt{6}) \)	✓	$4$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
552.1.h.b	$552$	$1$	552.h	552.h	$2$	$1$	$1$	$0.275$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-138}) \)	\(\Q(\sqrt{6}) \)	✓	$4$	$0$	\(1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
552.1.h.c	$552$	$1$	552.h	552.h	$2$	$2$	$2$	$0.275$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-23}) \)	None		$4$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}+q^{8}+\cdots\)
552.1.h.d	$552$	$1$	552.h	552.h	$2$	$2$	$2$	$0.275$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-23}) \)	None		$4$	$0$	\(1\)	\(1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)