Space of modular forms of level 156, weight 1, and Character 156.s

• Label: 156.1.s
• Level: $156$
• Weight: $1$
• Character orbit: 156.s
• Rep. character: $\chi_{156}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	156.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(28\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(156, [\chi])\).

	Total	New	Old
Modular forms	14	2	12
Cusp forms	2	2	0
Eisenstein series	12	0	12

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + q^{3} - 3 q^{7} - q^{9} + q^{13} - 2 q^{25} - 2 q^{27} + 2 q^{39} + q^{43} + 2 q^{49} - q^{61} + 3 q^{63} + 3 q^{67} - q^{75} + 2 q^{79} - q^{81} - 3 q^{91} - 3 q^{93} - 3 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(156, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
156.1.s.a	$156$	$1$	156.s	39.h	$6$	$2$	$1$	$0.078$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓	✓	✓	156.1.s.a	$4$	$0$	\(0\)	\(1\)	\(0\)	\(-3\)	$1$		\(q+\zeta_{6}q^{3}+(-1-\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots\)