Newform orbit 1980.2.f.b

• Label: 1980.2.f.b
• Level: $1980$
• Weight: $2$
• Character orbit: 1980.f
• Analytic conductor: $15.810$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1980.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.8103796002\)
Analytic rank:	\(0\)
Dimension:	\(40\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 4 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1871.1	−1.39225	−	0.248254i		0		1.87674	+	0.691264i			1.00000i		0			−	4.16820i	−2.44129	−	1.42832i		0		0.248254	−	1.39225i
1871.2	−1.39225	+	0.248254i		0		1.87674	−	0.691264i		−	1.00000i		0				4.16820i	−2.44129	+	1.42832i		0		0.248254	+	1.39225i
1871.3	−1.37691	−	0.322654i		0		1.79179	+	0.888535i		−	1.00000i		0			−	0.0719637i	−2.18045	−	1.80157i		0		−0.322654	+	1.37691i
1871.4	−1.37691	+	0.322654i		0		1.79179	−	0.888535i			1.00000i		0				0.0719637i	−2.18045	+	1.80157i		0		−0.322654	−	1.37691i
1871.5	−1.31419	−	0.522409i		0		1.45418	+	1.37309i		−	1.00000i		0				1.98169i	−1.19375	−	2.56417i		0		−0.522409	+	1.31419i
1871.6	−1.31419	+	0.522409i		0		1.45418	−	1.37309i			1.00000i		0			−	1.98169i	−1.19375	+	2.56417i		0		−0.522409	−	1.31419i
1871.7	−1.09271	−	0.897769i		0		0.388021	+	1.96200i			1.00000i		0				0.112424i	1.33743	−	2.49224i		0		0.897769	−	1.09271i
1871.8	−1.09271	+	0.897769i		0		0.388021	−	1.96200i		−	1.00000i		0			−	0.112424i	1.33743	+	2.49224i		0		0.897769	+	1.09271i
1871.9	−1.03817	−	0.960312i		0		0.155600	+	1.99394i		−	1.00000i		0			−	4.36619i	1.75326	−	2.21947i		0		−0.960312	+	1.03817i
1871.10	−1.03817	+	0.960312i		0		0.155600	−	1.99394i			1.00000i		0				4.36619i	1.75326	+	2.21947i		0		−0.960312	−	1.03817i
1871.11	−1.02572	−	0.973596i		0		0.104222	+	1.99728i			1.00000i		0				1.00680i	1.83764	−	2.15013i		0		0.973596	−	1.02572i
1871.12	−1.02572	+	0.973596i		0		0.104222	−	1.99728i		−	1.00000i		0			−	1.00680i	1.83764	+	2.15013i		0		0.973596	+	1.02572i
1871.13	−0.497594	−	1.32378i		0		−1.50480	+	1.31741i		−	1.00000i		0			−	2.37531i	2.49275	+	1.33649i		0		−1.32378	+	0.497594i
1871.14	−0.497594	+	1.32378i		0		−1.50480	−	1.31741i			1.00000i		0				2.37531i	2.49275	−	1.33649i		0		−1.32378	−	0.497594i
1871.15	−0.459058	−	1.33763i		0		−1.57853	+	1.22810i		−	1.00000i		0				3.16400i	2.36739	+	1.54773i		0		−1.33763	+	0.459058i
1871.16	−0.459058	+	1.33763i		0		−1.57853	−	1.22810i			1.00000i		0			−	3.16400i	2.36739	−	1.54773i		0		−1.33763	−	0.459058i
1871.17	−0.302390	−	1.38151i		0		−1.81712	+	0.835506i			1.00000i		0				3.30694i	1.70374	+	2.25772i		0		1.38151	−	0.302390i
1871.18	−0.302390	+	1.38151i		0		−1.81712	−	0.835506i		−	1.00000i		0			−	3.30694i	1.70374	−	2.25772i		0		1.38151	+	0.302390i
1871.19	−0.199078	−	1.40013i		0		−1.92074	+	0.557472i			1.00000i		0			−	0.448695i	1.16291	+	2.57830i		0		1.40013	−	0.199078i
1871.20	−0.199078	+	1.40013i		0		−1.92074	−	0.557472i		−	1.00000i		0				0.448695i	1.16291	−	2.57830i		0		1.40013	+	0.199078i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1980.2.f.b	yes	40
3.b	odd	2	1		1980.2.f.a	✓	40
4.b	odd	2	1		1980.2.f.a	✓	40
12.b	even	2	1	inner	1980.2.f.b	yes	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
1980.2.f.a	✓	40	3.b	odd	2	1
1980.2.f.a	✓	40	4.b	odd	2	1
1980.2.f.b	yes	40	1.a	even	1	1	trivial
1980.2.f.b	yes	40	12.b	even	2	1	inner