Newform orbit 2160.4.a.i

• Label: 2160.4.a.i
• Level: $2160$
• Weight: $4$
• Character orbit: 2160.a
• Self dual: yes
• Analytic conductor: $127.444$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$2160 = 2^{4} \cdot 3^{3} \cdot 5$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	2160.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$127.444125612$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 270)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 5 * q^5 + 22 * q^7 + 12 * q^11 + 38 * q^13 - 105 * q^17 + 157 * q^19 + 117 * q^23 + 25 * q^25 + 66 * q^29 + 25 * q^31 - 110 * q^35 + 314 * q^37 - 504 * q^41 - 380 * q^43 + 252 * q^47 + 141 * q^49 + 3 * q^53 - 60 * q^55 + 318 * q^59 + 293 * q^61 - 190 * q^65 + 322 * q^67 + 120 * q^71 + 44 * q^73 + 264 * q^77 - 917 * q^79 - 309 * q^83 + 525 * q^85 + 1272 * q^89 + 836 * q^91 - 785 * q^95 + 1328 * q^97

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

1.1

0

0

0

0

−5.00000

0

22.0000

0

0

0

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$-1$
$5$	$+1$

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2160.4.a.i		1
3.b	odd	2	1		2160.4.a.r		1
4.b	odd	2	1		270.4.a.g	yes	1
12.b	even	2	1		270.4.a.c	✓	1
20.d	odd	2	1		1350.4.a.l		1
20.e	even	4	2		1350.4.c.i		2
36.f	odd	6	2		810.4.e.k		2
36.h	even	6	2		810.4.e.s		2
60.h	even	2	1		1350.4.a.z		1
60.l	odd	4	2		1350.4.c.l		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
270.4.a.c	✓	1	12.b	even	2	1
270.4.a.g	yes	1	4.b	odd	2	1
810.4.e.k		2	36.f	odd	6	2
810.4.e.s		2	36.h	even	6	2
1350.4.a.l		1	20.d	odd	2	1
1350.4.a.z		1	60.h	even	2	1
1350.4.c.i		2	20.e	even	4	2
1350.4.c.l		2	60.l	odd	4	2
2160.4.a.i		1	1.a	even	1	1	trivial
2160.4.a.r		1	3.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(2160))$:

$T_{7} - 22$

$T_{11} - 12$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T + 5$
$7$	$T - 22$
$11$	$T - 12$