Space of modular forms of level 31, weight 1, and Character 31.b

• Label: 31.1.b
• Level: $31$
• Weight: $1$
• Character orbit: 31.b
• Rep. character: $\chi_{31}(30,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $2$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	31.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 31 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(2\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(31, [\chi])\).

	Total	New	Old
Modular forms	2	2	0
Cusp forms	1	1	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	1	0	0	0

Trace form

\( q - q^{2} - q^{5} - q^{7} + q^{8} + q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(31, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
31.1.b.a	$31$	$1$	31.b	31.b	$2$	$1$	$1$	$0.015$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-31}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(-1\)	$1$		\(q-q^{2}-q^{5}-q^{7}+q^{8}+q^{9}+q^{10}+\cdots\)