Newform orbit 1800.4.a.z

• Label: 1800.4.a.z
• Level: $1800$
• Weight: $4$
• Character orbit: 1800.a
• Self dual: yes
• Analytic conductor: $106.203$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$1800 = 2^{3} \cdot 3^{2} \cdot 5^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1800.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$106.203438010$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 72)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + 12 * q^7 - 64 * q^11 - 58 * q^13 + 32 * q^17 - 136 * q^19 - 128 * q^23 + 144 * q^29 + 20 * q^31 + 18 * q^37 + 288 * q^41 + 200 * q^43 + 384 * q^47 - 199 * q^49 + 496 * q^53 + 128 * q^59 - 458 * q^61 + 496 * q^67 - 512 * q^71 + 602 * q^73 - 768 * q^77 + 1108 * q^79 + 704 * q^83 + 960 * q^89 - 696 * q^91 - 206 * 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

0

0

12.0000

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	1800.4.a.z		1
3.b	odd	2	1		1800.4.a.ba		1
5.b	even	2	1		72.4.a.a	✓	1
5.c	odd	4	2		1800.4.f.b		2
15.d	odd	2	1		72.4.a.d	yes	1
15.e	even	4	2		1800.4.f.x		2
20.d	odd	2	1		144.4.a.a		1
40.e	odd	2	1		576.4.a.x		1
40.f	even	2	1		576.4.a.w		1
45.h	odd	6	2		648.4.i.a		2
45.j	even	6	2		648.4.i.l		2
60.h	even	2	1		144.4.a.f		1
120.i	odd	2	1		576.4.a.c		1
120.m	even	2	1		576.4.a.d		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
72.4.a.a	✓	1	5.b	even	2	1
72.4.a.d	yes	1	15.d	odd	2	1
144.4.a.a		1	20.d	odd	2	1
144.4.a.f		1	60.h	even	2	1
576.4.a.c		1	120.i	odd	2	1
576.4.a.d		1	120.m	even	2	1
576.4.a.w		1	40.f	even	2	1
576.4.a.x		1	40.e	odd	2	1
648.4.i.a		2	45.h	odd	6	2
648.4.i.l		2	45.j	even	6	2
1800.4.a.z		1	1.a	even	1	1	trivial
1800.4.a.ba		1	3.b	odd	2	1
1800.4.f.b		2	5.c	odd	4	2
1800.4.f.x		2	15.e	even	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1800))$:

$T_{7} - 12$

$T_{11} + 64$

$T_{17} - 32$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T$
$7$	$T - 12$
$11$	$T + 64$