Newform orbit 1800.4.a.j

• Label: 1800.4.a.j
• 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 120)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 10 * q^7 + 46 * q^11 + 34 * q^13 + 66 * q^17 + 104 * q^19 + 164 * q^23 - 224 * q^29 - 72 * q^31 + 22 * q^37 - 194 * q^41 - 108 * q^43 - 480 * q^47 - 243 * q^49 + 286 * q^53 - 426 * q^59 + 698 * q^61 - 328 * q^67 - 188 * q^71 + 740 * q^73 - 460 * q^77 + 1168 * q^79 + 412 * q^83 - 1206 * q^89 - 340 * q^91 + 1384 * 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

−10.0000

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.j		1
3.b	odd	2	1		600.4.a.b		1
5.b	even	2	1		1800.4.a.y		1
5.c	odd	4	2		360.4.f.c		2
12.b	even	2	1		1200.4.a.bh		1
15.d	odd	2	1		600.4.a.o		1
15.e	even	4	2		120.4.f.a	✓	2
20.e	even	4	2		720.4.f.g		2
60.h	even	2	1		1200.4.a.f		1
60.l	odd	4	2		240.4.f.b		2
120.q	odd	4	2		960.4.f.g		2
120.w	even	4	2		960.4.f.l		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
120.4.f.a	✓	2	15.e	even	4	2
240.4.f.b		2	60.l	odd	4	2
360.4.f.c		2	5.c	odd	4	2
600.4.a.b		1	3.b	odd	2	1
600.4.a.o		1	15.d	odd	2	1
720.4.f.g		2	20.e	even	4	2
960.4.f.g		2	120.q	odd	4	2
960.4.f.l		2	120.w	even	4	2
1200.4.a.f		1	60.h	even	2	1
1200.4.a.bh		1	12.b	even	2	1
1800.4.a.j		1	1.a	even	1	1	trivial
1800.4.a.y		1	5.b	even	2	1

Hecke kernels

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

$T_{7} + 10$

$T_{11} - 46$

$T_{17} - 66$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T$
$7$	$T + 10$
$11$	$T - 46$