Space of modular forms of level 20, weight 7, and Character 20.b

• Label: 20.7.b
• Level: $20$
• Weight: $7$
• Character orbit: 20.b
• Rep. character: $\chi_{20}(11,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $21$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(21\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(20, [\chi])\).

	Total	New	Old
Modular forms	20	12	8
Cusp forms	16	12	4
Eisenstein series	4	0	4

Trace form

\( 12 q - 10 q^{2} + 156 q^{4} - 672 q^{6} + 440 q^{8} - 1996 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(20, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
20.7.b.a	$20$	$7$	20.b	4.b	$2$	$12$	$12$	$4.601$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-10\)	\(0\)	\(0\)	\(0\)	$2^{33}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{2})q^{2}+(-\beta _{2}-\beta _{6})q^{3}+(13+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(20, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 2}\)