Space of modular forms of level 20, weight 9, and Character 20.f

• Label: 20.9.f
• Level: $20$
• Weight: $9$
• Character orbit: 20.f
• Rep. character: $\chi_{20}(13,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $27$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	20.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(27\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(20, [\chi])\).

	Total	New	Old
Modular forms	54	8	46
Cusp forms	42	8	34
Eisenstein series	12	0	12

Trace form

\( 8 q - 70 q^{3} + 894 q^{5} - 2030 q^{7} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(20, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
20.9.f.a	$20$	$9$	20.f	5.c	$4$	$8$	$4$	$8.148$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(-70\)	\(894\)	\(-2030\)	$2^{13}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-9-9\beta _{1}+\beta _{2})q^{3}+(112-58\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(20, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(20, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)