Space of modular forms of level 2156, weight 1, and Character 2156.m

• Label: 2156.1.m
• Level: $2156$
• Weight: $1$
• Character orbit: 2156.m
• Rep. character: $\chi_{2156}(1011,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $336$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2156.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 308 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(336\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2156, [\chi])\).

	Total	New	Old
Modular forms	36	20	16
Cusp forms	4	4	0
Eisenstein series	32	16	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q - 2 q^{4} + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2156, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2156.1.m.a	$2156$	$1$	2156.m	308.m	$6$	$2$	$1$	$1.076$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-77}) \)	\(\Q(\sqrt{11}) \)					308.1.g.a	$8$	$0$	\(-1\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{8}-\zeta_{6}^{2}q^{9}+\cdots\)
2156.1.m.b	$2156$	$1$	2156.m	308.m	$6$	$2$	$1$	$1.076$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-77}) \)	\(\Q(\sqrt{11}) \)					308.1.g.a	$8$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}-\zeta_{6}^{2}q^{9}+\cdots\)