Newform orbit 160.3.e.b

• Label: 160.3.e.b
• Level: $160$
• Weight: $3$
• Character orbit: 160.e
• Self dual: yes
• Analytic conductor: $4.360$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -40
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	160.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(4.35968422976\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\)

\(=\)

q + 5 * q^5 - 6 * q^7 + 9 * q^9 + 18 * q^11 - 6 * q^13 + 2 * q^19 + 26 * q^23 + 25 * q^25 - 30 * q^35 - 54 * q^37 - 78 * q^41 + 45 * q^45 - 86 * q^47 - 13 * q^49 + 74 * q^53 + 90 * q^55 - 78 * q^59 - 54 * q^63 - 30 * q^65 - 108 * q^77 + 81 * q^81 + 18 * q^89 + 36 * q^91 + 10 * q^95 + 162 * q^99

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).

\(n\)	\(31\)	\(97\)	\(101\)
\(\chi(n)\)	\(-1\)	\(-1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

79.1

0

0

0

0

5.00000

0

−6.00000

0

9.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
40.e	odd	2	1	CM by \(\Q(\sqrt{-10}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	160.3.e.b		1
3.b	odd	2	1		1440.3.p.a		1
4.b	odd	2	1		40.3.e.a	✓	1
5.b	even	2	1		160.3.e.a		1
5.c	odd	4	2		800.3.g.c		2
8.b	even	2	1		40.3.e.b	yes	1
8.d	odd	2	1		160.3.e.a		1
12.b	even	2	1		360.3.p.b		1
15.d	odd	2	1		1440.3.p.b		1
16.e	even	4	2		1280.3.h.c		2
16.f	odd	4	2		1280.3.h.b		2
20.d	odd	2	1		40.3.e.b	yes	1
20.e	even	4	2		200.3.g.c		2
24.f	even	2	1		1440.3.p.b		1
24.h	odd	2	1		360.3.p.a		1
40.e	odd	2	1	CM	160.3.e.b		1
40.f	even	2	1		40.3.e.a	✓	1
40.i	odd	4	2		200.3.g.c		2
40.k	even	4	2		800.3.g.c		2
60.h	even	2	1		360.3.p.a		1
80.k	odd	4	2		1280.3.h.c		2
80.q	even	4	2		1280.3.h.b		2
120.i	odd	2	1		360.3.p.b		1
120.m	even	2	1		1440.3.p.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
40.3.e.a	✓	1	4.b	odd	2	1
40.3.e.a	✓	1	40.f	even	2	1
40.3.e.b	yes	1	8.b	even	2	1
40.3.e.b	yes	1	20.d	odd	2	1
160.3.e.a		1	5.b	even	2	1
160.3.e.a		1	8.d	odd	2	1
160.3.e.b		1	1.a	even	1	1	trivial
160.3.e.b		1	40.e	odd	2	1	CM
200.3.g.c		2	20.e	even	4	2
200.3.g.c		2	40.i	odd	4	2
360.3.p.a		1	24.h	odd	2	1
360.3.p.a		1	60.h	even	2	1
360.3.p.b		1	12.b	even	2	1
360.3.p.b		1	120.i	odd	2	1
800.3.g.c		2	5.c	odd	4	2
800.3.g.c		2	40.k	even	4	2
1280.3.h.b		2	16.f	odd	4	2
1280.3.h.b		2	80.q	even	4	2
1280.3.h.c		2	16.e	even	4	2
1280.3.h.c		2	80.k	odd	4	2
1440.3.p.a		1	3.b	odd	2	1
1440.3.p.a		1	120.m	even	2	1
1440.3.p.b		1	15.d	odd	2	1
1440.3.p.b		1	24.f	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(160, [\chi])\):

\( T_{3} \)

\( T_{7} + 6 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T \)
$3$	\( T \)
$5$	\( T - 5 \)
$7$	\( T + 6 \)
$11$	\( T - 18 \)