Space of modular forms of level 196, weight 1, and Character 196.g

• Label: 196.1.g
• Level: $196$
• Weight: $1$
• Character orbit: 196.g
• Rep. character: $\chi_{196}(67,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	196.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
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 \(M_{1}(196, [\chi])\).

	Total	New	Old
Modular forms	18	10	8
Cusp forms	2	2	0
Eisenstein series	16	8	8

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

\( 2 q + q^{2} - q^{4} - 2 q^{8} - q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(196, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
196.1.g.a	$196$	$1$	196.g	28.g	$6$	$2$	$1$	$0.098$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \)	\(\Q(\sqrt{7}) \)		✓	✓	✓	196.1.c.a	$8$	$0$	\(1\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots\)