Newform orbit 4020.2.g.c

• Label: 4020.2.g.c
• Level: $4020$
• Weight: $2$
• Character orbit: 4020.g
• Analytic conductor: $32.100$
• Analytic rank: $0$
• Dimension: $38$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(32.0998616126\)
Analytic rank:	\(0\)
Dimension:	\(38\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 38 q - 2 q^{5} - 38 q^{9}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1609.1		0			−	1.00000i		0		−2.23543	+	0.0533841i		0			−	4.50874i		0		−1.00000				0
1609.2		0			−	1.00000i		0		−2.22744	+	0.196195i		0				0.128273i		0		−1.00000				0
1609.3		0			−	1.00000i		0		−2.06455	+	0.858848i		0				3.58783i		0		−1.00000				0
1609.4		0			−	1.00000i		0		−2.02556	−	0.947153i		0				2.95752i		0		−1.00000				0
1609.5		0			−	1.00000i		0		−1.48830	+	1.66882i		0			−	2.27974i		0		−1.00000				0
1609.6		0			−	1.00000i		0		−0.953985	−	2.02235i		0				5.11769i		0		−1.00000				0
1609.7		0			−	1.00000i		0		−0.847850	+	2.06909i		0				3.67313i		0		−1.00000				0
1609.8		0			−	1.00000i		0		−0.676225	−	2.13137i		0			−	4.23231i		0		−1.00000				0
1609.9		0			−	1.00000i		0		−0.599682	−	2.15415i		0				0.0778518i		0		−1.00000				0
1609.10		0			−	1.00000i		0		−0.504884	−	2.17832i		0			−	3.91807i		0		−1.00000				0
1609.11		0			−	1.00000i		0		−0.471887	+	2.18571i		0			−	1.05400i		0		−1.00000				0
1609.12		0			−	1.00000i		0		0.145309	+	2.23134i		0			−	1.12842i		0		−1.00000				0
1609.13		0			−	1.00000i		0		1.17292	−	1.90375i		0				2.37828i		0		−1.00000				0
1609.14		0			−	1.00000i		0		1.34274	+	1.78803i		0				0.521655i		0		−1.00000				0
1609.15		0			−	1.00000i		0		1.96436	+	1.06831i		0			−	3.03191i		0		−1.00000				0
1609.16		0			−	1.00000i		0		1.96624	+	1.06486i		0				4.32230i		0		−1.00000				0
1609.17		0			−	1.00000i		0		2.08125	−	0.817560i		0				3.41849i		0		−1.00000				0
1609.18		0			−	1.00000i		0		2.20926	−	0.345224i		0				0.0620642i		0		−1.00000				0
1609.19		0			−	1.00000i		0		2.21373	+	0.315287i		0			−	0.0918930i		0		−1.00000				0
1609.20		0				1.00000i		0		−2.23543	−	0.0533841i		0				4.50874i		0		−1.00000				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	4020.2.g.c	✓	38
5.b	even	2	1	inner	4020.2.g.c	✓	38

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
4020.2.g.c	✓	38	1.a	even	1	1	trivial
4020.2.g.c	✓	38	5.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T7^38 + 168*T7^36 + 12756*T7^34 + 579200*T7^32 + 17532664*T7^30 + 373287946*T7^28 + 5745701054*T7^26 + 64680970638*T7^24 + 532307001632*T7^22 + 3165477805940*T7^20 + 13274065898009*T7^18 + 37661766331674*T7^16 + 67667049775571*T7^14 + 69424104965230*T7^12 + 34950409161221*T7^10 + 6212836982244*T7^8 + 189289292036*T7^6 + 2130360576*T7^4 + 9998336*T7^2 + 16384