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

• Label: 20.20.c
• Level: $20$
• Weight: $20$
• Character orbit: 20.c
• Rep. character: $\chi_{20}(9,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 20 \)
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:			\(60\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	60	10	50
Cusp forms	54	10	44
Eisenstein series	6	0	6

Trace form

\( 10 q - 897466 q^{5} - 2194749290 q^{9} + O(q^{10}) \)

Decomposition of \(S_{20}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
20.20.c.a	$20$	$20$	20.c	5.b	$2$	$10$	$10$	$45.763$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	20.20.c.a	$2$	$0$	\(0\)	\(0\)	\(-897466\)	\(0\)	$2^{56}\cdot 3^{6}\cdot 5^{17}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-89747-8\beta _{1}+\beta _{2})q^{5}+\cdots\)

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

\( S_{20}^{\mathrm{old}}(20, [\chi]) \simeq \) \(S_{20}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)