Space of modular forms of level 1988, weight 1, and Character 1988.g

• Label: 1988.1.g
• Level: $1988$
• Weight: $1$
• Character orbit: 1988.g
• Rep. character: $\chi_{1988}(1987,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $8$
• Sturm bound: $288$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1988 = 2^{2} \cdot 7 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1988.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1988 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(288\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1988, [\chi])\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	10	10	0
Eisenstein series	4	4	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	10	0	0	0

Trace form

\( 10 q - 2 q^{2} + 10 q^{4} - 2 q^{8} + 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1988, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1988.1.g.a	$1988$	$1$	1988.g	1988.g	$2$	$1$	$1$	$0.992$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-497}) \)	\(\Q(\sqrt{71}) \)	✓	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)	$1$		\(q-q^{2}+q^{4}-q^{7}-q^{8}-q^{9}+2q^{11}+\cdots\)
1988.1.g.b	$1988$	$1$	1988.g	1988.g	$2$	$1$	$1$	$0.992$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-497}) \)	\(\Q(\sqrt{71}) \)	✓	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)	$1$		\(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{9}-2q^{11}+\cdots\)
1988.1.g.c	$1988$	$1$	1988.g	1988.g	$2$	$1$	$1$	$0.992$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-497}) \)	None	✓	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
1988.1.g.d	$1988$	$1$	1988.g	1988.g	$2$	$1$	$1$	$0.992$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-497}) \)	None	✓	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(1\)	$1$		\(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
1988.1.g.e	$1988$	$1$	1988.g	1988.g	$2$	$1$	$1$	$0.992$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-497}) \)	None	✓	$2$	$0$	\(1\)	\(1\)	\(0\)	\(-1\)	$1$		\(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
1988.1.g.f	$1988$	$1$	1988.g	1988.g	$2$	$1$	$1$	$0.992$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-497}) \)	None	✓	$2$	$0$	\(1\)	\(1\)	\(0\)	\(1\)	$1$		\(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
1988.1.g.g	$1988$	$1$	1988.g	1988.g	$2$	$2$	$2$	$0.992$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-497}) \)	None	✓	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{7}-q^{8}+\cdots\)
1988.1.g.h	$1988$	$1$	1988.g	1988.g	$2$	$2$	$2$	$0.992$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-497}) \)	None	✓	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(2\)	$1$		\(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+q^{7}-q^{8}+\cdots\)