Space of modular forms of level 131, weight 1, and Character 131.b

• Label: 131.1.b
• Level: $131$
• Weight: $1$
• Character orbit: 131.b
• Rep. character: $\chi_{131}(130,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $11$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 131 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	131.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 131 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(11\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(131, [\chi])\).

	Total	New	Old
Modular forms	3	3	0
Cusp forms	2	2	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	2	0	0	0

Trace form

2 * q - q^3 + 2 * q^4 - q^5 - q^7 + q^9 - q^11 - q^12 - q^13 - 2 * q^15 + 2 * q^16 - q^20 - 2 * q^21 + q^25 - 2 * q^27 - q^28 + 3 * q^33 + 3 * q^35 + q^36 + 3 * q^39 - q^41 - q^43 - q^44 + 2 * q^45 - q^48 + q^49 - q^52 + 4 * q^53 - 2 * q^55 - q^59 - 2 * q^60 - q^61 + 2 * q^63 + 2 * q^64 - 2 * q^65 + 2 * q^75 - 2 * q^77 - q^80 - 2 * q^84 + 4 * q^89 - 2 * q^91 - 3 * q^99

Decomposition of \(S_{1}^{\mathrm{new}}(131, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
131.1.b.a	$131$	$1$	131.b	131.b	$2$	$2$	$2$	$0.065$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-131}) \)	None	✓	✓	✓	✓	131.1.b.a	$2$	$0$	\(0\)	\(-1\)	\(-1\)	\(-1\)	$1$		\(q+(-1+\beta )q^{3}+q^{4}-\beta q^{5}-\beta q^{7}+\cdots\)