Space of modular forms of level 556, weight 1, and Character 556.c

• Label: 556.1.c
• Level: $556$
• Weight: $1$
• Character orbit: 556.c
• Rep. character: $\chi_{556}(277,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $1$
• Sturm bound: $70$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 556 = 2^{2} \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	556.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 139 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(70\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(556, [\chi])\).

	Total	New	Old
Modular forms	9	3	6
Cusp forms	6	3	3
Eisenstein series	3	0	3

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	3	0	0	0

Trace form

\( 3 q + 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(556, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
556.1.c.a	$556$	$1$	556.c	139.b	$2$	$3$	$3$	$0.277$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-139}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}+(\beta _{1}-\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(556, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(556, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(139, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(278, [\chi])\)\(^{\oplus 2}\)