Space of modular forms of level 200, weight 1, and Character 200.g

• Label: 200.1.g
• Level: $200$
• Weight: $1$
• Character orbit: 200.g
• Rep. character: $\chi_{200}(51,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $30$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	200.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(30\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(200, [\chi])\).

	Total	New	Old
Modular forms	8	5	3
Cusp forms	2	2	0
Eisenstein series	6	3	3

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

\( 2 q + 2 q^{4} - 2 q^{6} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(200, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
200.1.g.a	$200$	$1$	200.g	8.d	$2$	$1$	$1$	$0.100$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None	✓	✓			200.1.g.a	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-q^{11}+\cdots\)
200.1.g.b	$200$	$1$	200.g	8.d	$2$	$1$	$1$	$0.100$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None	✓	✓			200.1.g.a	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-q^{11}+\cdots\)