Space of modular forms of level 20, weight 5, and Character 20.d

• Label: 20.5.d
• Level: $20$
• Weight: $5$
• Character orbit: 20.d
• Rep. character: $\chi_{20}(19,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $15$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
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:			\(15\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(20, [\chi])\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	10	10	0
Eisenstein series	4	4	0

Trace form

\( 10 q - 16 q^{4} + 10 q^{5} - 16 q^{6} + 158 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(20, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
20.5.d.a	$20$	$5$	20.d	20.d	$2$	$1$	$1$	$2.067$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	$2$	$0$	\(-4\)	\(2\)	\(25\)	\(82\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-4q^{2}+2q^{3}+2^{4}q^{4}+5^{2}q^{5}-8q^{6}+\cdots\)
20.5.d.b	$20$	$5$	20.d	20.d	$2$	$1$	$1$	$2.067$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	$2$	$0$	\(4\)	\(-2\)	\(25\)	\(-82\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{2}-2q^{3}+2^{4}q^{4}+5^{2}q^{5}-8q^{6}+\cdots\)
20.5.d.c	$20$	$5$	20.d	20.d	$2$	$8$	$8$	$2.067$	8.0.\(\cdots\).2	None		$4$	$0$	\(0\)	\(0\)	\(-40\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-6+\beta _{3})q^{4}+(-5+\cdots)q^{5}+\cdots\)