Newform orbit 200.8.a.f

• Label: 200.8.a.f
• Level: $200$
• Weight: $8$
• Character orbit: 200.a
• Self dual: yes
• Analytic conductor: $62.477$
• Analytic rank: $1$
• 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:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 40)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + 34 * q^3 + 106 * q^7 - 1031 * q^9 - 1324 * q^11 + 8828 * q^13 - 24000 * q^17 - 4876 * q^19 + 3604 * q^21 + 46646 * q^23 - 109412 * q^27 - 110902 * q^29 - 247680 * q^31 - 45016 * q^33 + 360092 * q^37 + 300152 * q^39 + 104402 * q^41 - 713622 * q^43 + 156882 * q^47 - 812307 * q^49 - 816000 * q^51 - 1066268 * q^53 - 165784 * q^57 + 832572 * q^59 + 529070 * q^61 - 109286 * q^63 - 4174418 * q^67 + 1585964 * q^69 + 5176568 * q^71 + 237976 * q^73 - 140344 * q^77 - 3742736 * q^79 - 1465211 * q^81 - 7861886 * q^83 - 3770668 * q^87 + 4300854 * q^89 + 935768 * q^91 - 8421120 * q^93 - 1147792 * q^97 + 1365044 * 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

34.0000

0

0

0

106.000

0

−1031.00

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.f		1
4.b	odd	2	1		400.8.a.h		1
5.b	even	2	1		200.8.a.c		1
5.c	odd	4	2		40.8.c.a	✓	2
15.e	even	4	2		360.8.f.a		2
20.d	odd	2	1		400.8.a.n		1
20.e	even	4	2		80.8.c.b		2
40.i	odd	4	2		320.8.c.b		2
40.k	even	4	2		320.8.c.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
40.8.c.a	✓	2	5.c	odd	4	2
80.8.c.b		2	20.e	even	4	2
200.8.a.c		1	5.b	even	2	1
200.8.a.f		1	1.a	even	1	1	trivial
320.8.c.a		2	40.k	even	4	2
320.8.c.b		2	40.i	odd	4	2
360.8.f.a		2	15.e	even	4	2
400.8.a.h		1	4.b	odd	2	1
400.8.a.n		1	20.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{3} - 34$ acting on $S_{8}^{\mathrm{new}}(\Gamma_0(200))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T - 34$
$5$	$T$
$7$	$T - 106$
$11$	$T + 1324$