Space of modular forms of level 61, weight 4, and Character 61.b

• Label: 61.4.b
• Level: $61$
• Weight: $4$
• Character orbit: 61.b
• Rep. character: $\chi_{61}(60,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	61.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 61 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(20\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(61, [\chi])\).

	Total	New	Old
Modular forms	16	16	0
Cusp forms	14	14	0
Eisenstein series	2	2	0

Trace form

\( 14 q - 2 q^{3} - 38 q^{4} - 14 q^{5} + 116 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(61, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
61.4.b.a	$61$	$4$	61.b	61.b	$2$	$14$	$14$	$3.599$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓	✓	✓	61.4.b.a	$2$	$0$	\(0\)	\(-2\)	\(-14\)	\(0\)	$2^{2}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-3+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)