Space of modular forms of level 20, weight 11, and Character 20.d

• Label: 20.11.d
• Level: $20$
• Weight: $11$
• Character orbit: 20.d
• Rep. character: $\chi_{20}(19,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $4$
• Sturm bound: $33$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	20.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(33\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(20, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	28	28	0
Eisenstein series	4	4	0

Trace form

\( 28 q + 608 q^{4} + 1556 q^{5} - 4480 q^{6} + 472388 q^{9} + O(q^{10}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(20, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
20.11.d.a	$20$	$11$	20.d	20.d	$2$	$1$	$1$	$12.707$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	$2$	$0$	\(-32\)	\(-236\)	\(-3125\)	\(-33364\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2^{5}q^{2}-236q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
20.11.d.b	$20$	$11$	20.d	20.d	$2$	$1$	$1$	$12.707$	\(\Q\)	\(\Q(\sqrt{-5}) \)	✓	$2$	$0$	\(32\)	\(236\)	\(-3125\)	\(33364\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{5}q^{2}+236q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
20.11.d.c	$20$	$11$	20.d	20.d	$2$	$2$	$2$	$12.707$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(-474\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+8iq^{2}-2^{10}q^{4}+(-237+779i)q^{5}+\cdots\)
20.11.d.d	$20$	$11$	20.d	20.d	$2$	$24$	$24$	$12.707$		None		$4$	$0$	\(0\)	\(0\)	\(8280\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$