Space of modular forms of level 20, weight 4, and Character 20.c

• Label: 20.4.c
• Level: $20$
• Weight: $4$
• Character orbit: 20.c
• Rep. character: $\chi_{20}(9,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	20.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(20, [\chi])\).

	Total	New	Old
Modular forms	12	2	10
Cusp forms	6	2	4
Eisenstein series	6	0	6

Trace form

\( 2 q + 14 q^{5} - 98 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(20, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
20.4.c.a	$20$	$4$	20.c	5.b	$2$	$2$	$2$	$1.180$	\(\Q(\sqrt{-19}) \)	None		✓	✓	✓	20.4.c.a	$2$	$0$	\(0\)	\(0\)	\(14\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}+(7+\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(20, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)