Space of modular forms of level 1931, weight 1, and Character 1931.b

• Label: 1931.1.b
• Level: $1931$
• Weight: $1$
• Character orbit: 1931.b
• Rep. character: $\chi_{1931}(1930,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $161$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1931 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1931.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1931 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(161\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1931, [\chi])\).

	Total	New	Old
Modular forms	13	13	0
Cusp forms	12	12	0
Eisenstein series	1	1	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	2	0

Trace form

\( 12 q - q^{3} + 8 q^{4} - 3 q^{5} + q^{7} + 7 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1931, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1931.1.b.a	$1931$	$1$	1931.b	1931.b	$2$	$1$	$1$	$0.964$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1931}) \)	None	✓	$2$	$0$	\(0\)	\(2\)	\(-1\)	\(-1\)	$1$		\(q+2q^{3}+q^{4}-q^{5}-q^{7}+3q^{9}-q^{11}+\cdots\)
1931.1.b.b	$1931$	$1$	1931.b	1931.b	$2$	$2$	$2$	$0.964$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)	$1$		\(q-\beta q^{2}-q^{4}-q^{5}+q^{7}-q^{9}+\beta q^{10}+\cdots\)
1931.1.b.c	$1931$	$1$	1931.b	1931.b	$2$	$3$	$3$	$0.964$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-1931}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)	$1$		\(q-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
1931.1.b.d	$1931$	$1$	1931.b	1931.b	$2$	$6$	$6$	$0.964$	\(\Q(\zeta_{21})^+\)	$D_{21}$	\(\Q(\sqrt{-1931}) \)	None	✓	$2$	$0$	\(0\)	\(-2\)	\(1\)	\(1\)	$1$		\(q+\beta _{3}q^{3}+q^{4}+\beta _{4}q^{5}+(-\beta _{2}+\beta _{5})q^{7}+\cdots\)