Newform orbit 200.10.a.a

• Label: 200.10.a.a
• Level: $200$
• Weight: $10$
• Character orbit: 200.a
• Self dual: yes
• Analytic conductor: $103.007$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$200 = 2^{3} \cdot 5^{2}$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	200.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$103.007167233$
Analytic rank:	$1$
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 - 68 * q^3 - 10248 * q^7 - 15059 * q^9 + 3916 * q^11 + 176594 * q^13 - 148370 * q^17 + 499796 * q^19 + 696864 * q^21 + 1889768 * q^23 + 2362456 * q^27 - 920898 * q^29 + 1379360 * q^31 - 266288 * q^33 - 5064966 * q^37 - 12008392 * q^39 - 24100758 * q^41 - 25785196 * q^43 + 60790224 * q^47 + 64667897 * q^49 + 10089160 * q^51 - 29496214 * q^53 - 33986128 * q^57 + 51819388 * q^59 + 33426910 * q^61 + 154324632 * q^63 - 144856196 * q^67 - 128504224 * q^69 + 68397128 * q^71 - 168216202 * q^73 - 40131168 * q^77 + 235398736 * q^79 + 135759289 * q^81 + 64639852 * q^83 + 62621064 * q^87 - 78782694 * q^89 - 1809735312 * q^91 - 93796480 * q^93 + 24113566 * q^97 - 58971044 * 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

−68.0000

0

0

0

−10248.0

0

−15059.0

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	200.10.a.a		1
4.b	odd	2	1		400.10.a.i		1
5.b	even	2	1		8.10.a.b	✓	1
5.c	odd	4	2		200.10.c.a		2
15.d	odd	2	1		72.10.a.a		1
20.d	odd	2	1		16.10.a.b		1
20.e	even	4	2		400.10.c.f		2
35.c	odd	2	1		392.10.a.a		1
40.e	odd	2	1		64.10.a.g		1
40.f	even	2	1		64.10.a.c		1
60.h	even	2	1		144.10.a.b		1
80.k	odd	4	2		256.10.b.k		2
80.q	even	4	2		256.10.b.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
8.10.a.b	✓	1	5.b	even	2	1
16.10.a.b		1	20.d	odd	2	1
64.10.a.c		1	40.f	even	2	1
64.10.a.g		1	40.e	odd	2	1
72.10.a.a		1	15.d	odd	2	1
144.10.a.b		1	60.h	even	2	1
200.10.a.a		1	1.a	even	1	1	trivial
200.10.c.a		2	5.c	odd	4	2
256.10.b.a		2	80.q	even	4	2
256.10.b.k		2	80.k	odd	4	2
392.10.a.a		1	35.c	odd	2	1
400.10.a.i		1	4.b	odd	2	1
400.10.c.f		2	20.e	even	4	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{3} + 68$ acting on $S_{10}^{\mathrm{new}}(\Gamma_0(200))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T + 68$
$5$	$T$
$7$	$T + 10248$
$11$	$T - 3916$