Space of modular forms of level 20, weight 3, and Character 20.d

• Label: 20.3.d
• Level: $20$
• Weight: $3$
• Character orbit: 20.d
• Rep. character: $\chi_{20}(19,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $3$
• Sturm bound: $9$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
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:			\(9\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(20, [\chi])\).

	Total	New	Old
Modular forms	8	8	0
Cusp forms	4	4	0
Eisenstein series	4	4	0

Trace form

\( 4 q - 4 q^{5} - 16 q^{6} - 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(20, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
20.3.d.a	$20$	$3$	20.d	20.d	$2$	$1$	$1$	$0.545$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	$2$	$0$	\(-2\)	\(4\)	\(-5\)	\(-4\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}+4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.b	$20$	$3$	20.d	20.d	$2$	$1$	$1$	$0.545$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	$2$	$0$	\(2\)	\(-4\)	\(-5\)	\(4\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}-4q^{3}+4q^{4}-5q^{5}-8q^{6}+\cdots\)
20.3.d.c	$20$	$3$	20.d	20.d	$2$	$2$	$2$	$0.545$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{2}-4q^{4}+(3-2i)q^{5}-4iq^{8}+\cdots\)