Newform orbit 200.8.a.i

• Label: 200.8.a.i
• Level: $200$
• Weight: $8$
• Character orbit: 200.a
• Self dual: yes
• Analytic conductor: $62.477$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$200 = 2^{3} \cdot 5^{2}$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	200.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$62.4770050968$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 8)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + 84 * q^3 + 456 * q^7 + 4869 * q^9 - 2524 * q^11 + 10778 * q^13 + 11150 * q^17 + 4124 * q^19 + 38304 * q^21 - 81704 * q^23 + 225288 * q^27 + 99798 * q^29 - 40480 * q^31 - 212016 * q^33 + 419442 * q^37 + 905352 * q^39 + 141402 * q^41 + 690428 * q^43 + 682032 * q^47 - 615607 * q^49 + 936600 * q^51 - 1813118 * q^53 + 346416 * q^57 - 966028 * q^59 + 1887670 * q^61 + 2220264 * q^63 - 2965868 * q^67 - 6863136 * q^69 - 2548232 * q^71 + 1680326 * q^73 - 1150944 * q^77 + 4038064 * q^79 + 8275689 * q^81 + 5385764 * q^83 + 8383032 * q^87 - 6473046 * q^89 + 4914768 * q^91 - 3400320 * q^93 + 6065758 * q^97 - 12289356 * q^99

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

84.0000

0

0

0

456.000

0

4869.00

0

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$5$	$+1$

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	200.8.a.i		1
4.b	odd	2	1		400.8.a.b		1
5.b	even	2	1		8.8.a.a	✓	1
5.c	odd	4	2		200.8.c.a		2
15.d	odd	2	1		72.8.a.d		1
20.d	odd	2	1		16.8.a.c		1
20.e	even	4	2		400.8.c.b		2
35.c	odd	2	1		392.8.a.d		1
40.e	odd	2	1		64.8.a.a		1
40.f	even	2	1		64.8.a.g		1
60.h	even	2	1		144.8.a.g		1
80.k	odd	4	2		256.8.b.c		2
80.q	even	4	2		256.8.b.e		2
120.i	odd	2	1		576.8.a.j		1
120.m	even	2	1		576.8.a.k		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
8.8.a.a	✓	1	5.b	even	2	1
16.8.a.c		1	20.d	odd	2	1
64.8.a.a		1	40.e	odd	2	1
64.8.a.g		1	40.f	even	2	1
72.8.a.d		1	15.d	odd	2	1
144.8.a.g		1	60.h	even	2	1
200.8.a.i		1	1.a	even	1	1	trivial
200.8.c.a		2	5.c	odd	4	2
256.8.b.c		2	80.k	odd	4	2
256.8.b.e		2	80.q	even	4	2
392.8.a.d		1	35.c	odd	2	1
400.8.a.b		1	4.b	odd	2	1
400.8.c.b		2	20.e	even	4	2
576.8.a.j		1	120.i	odd	2	1
576.8.a.k		1	120.m	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{3} - 84$ acting on $S_{8}^{\mathrm{new}}(\Gamma_0(200))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T - 84$
$5$	$T$
$7$	$T - 456$
$11$	$T + 2524$