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

• Label: 20.9.d
• Level: $20$
• Weight: $9$
• Character orbit: 20.d
• Rep. character: $\chi_{20}(19,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $3$
• Sturm bound: $27$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	20.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(27\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	26	26	0
Cusp forms	22	22	0
Eisenstein series	4	4	0

Trace form

\( 22 q - 240 q^{4} - 170 q^{5} - 1648 q^{6} + 39362 q^{9} + O(q^{10}) \)

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.d.a	$20$	$9$	20.d	20.d	$2$	$1$	$1$	$8.148$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	$2$	$0$	\(-16\)	\(158\)	\(625\)	\(-1922\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{4}q^{2}+158q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots\)
20.9.d.b	$20$	$9$	20.d	20.d	$2$	$1$	$1$	$8.148$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	$2$	$0$	\(16\)	\(-158\)	\(625\)	\(1922\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}q^{2}-158q^{3}+2^{8}q^{4}+5^{4}q^{5}+\cdots\)
20.9.d.c	$20$	$9$	20.d	20.d	$2$	$20$	$20$	$8.148$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(-1420\)	\(0\)	$2^{74}\cdot 3^{4}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{6})q^{3}+(-38+\beta _{2}+\cdots)q^{4}+\cdots\)