Newform orbit 160.11.e.b

• Label: 160.11.e.b
• Level: $160$
• Weight: $11$
• Character orbit: 160.e
• Self dual: yes
• Analytic conductor: $101.657$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -40
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$160 = 2^{5} \cdot 5$
Weight:	$k$	$=$	$11$
Character orbit:	$[\chi]$	$=$	160.e (of order $2$, degree $1$, not minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$101.657160428$
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 + 3125 * q^5 - 26886 * q^7 + 59049 * q^9 - 321102 * q^11 - 682086 * q^13 + 1288802 * q^19 + 1772186 * q^23 + 9765625 * q^25 - 84018750 * q^35 + 112652586 * q^37 - 611598 * q^41 + 184528125 * q^45 + 222705514 * q^47 + 440381747 * q^49 - 552886486 * q^53 - 1003443750 * q^55 + 646632402 * q^59 - 1587591414 * q^63 - 2131518750 * q^65 + 8633148372 * q^77 + 3486784401 * q^81 + 5417714898 * q^89 + 18338564196 * q^91 + 4027506250 * q^95 - 18960751998 * 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

3125.00

0

−26886.0

0

59049.0

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	160.11.e.b		1
4.b	odd	2	1		40.11.e.a	✓	1
5.b	even	2	1		160.11.e.a		1
8.b	even	2	1		40.11.e.b	yes	1
8.d	odd	2	1		160.11.e.a		1
20.d	odd	2	1		40.11.e.b	yes	1
40.e	odd	2	1	CM	160.11.e.b		1
40.f	even	2	1		40.11.e.a	✓	1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
40.11.e.a	✓	1	4.b	odd	2	1
40.11.e.a	✓	1	40.f	even	2	1
40.11.e.b	yes	1	8.b	even	2	1
40.11.e.b	yes	1	20.d	odd	2	1
160.11.e.a		1	5.b	even	2	1
160.11.e.a		1	8.d	odd	2	1
160.11.e.b		1	1.a	even	1	1	trivial
160.11.e.b		1	40.e	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{11}^{\mathrm{new}}(160, [\chi])$:

$T_{3}$

$T_{7} + 26886$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T - 3125$
$7$	$T + 26886$
$11$	$T + 321102$