Newform orbit 8.10.a.a

• Label: 8.10.a.a
• Level: $8$
• Weight: $10$
• Character orbit: 8.a
• Self dual: yes
• Analytic conductor: $4.120$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$8 = 2^{3}$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	8.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$4.12028668931$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 60 * q^3 - 2074 * q^5 - 4344 * q^7 - 16083 * q^9 + 93644 * q^11 - 12242 * q^13 + 124440 * q^15 - 319598 * q^17 - 553516 * q^19 + 260640 * q^21 - 712936 * q^23 + 2348351 * q^25 + 2145960 * q^27 + 2075838 * q^29 - 6420448 * q^31 - 5618640 * q^33 + 9009456 * q^35 - 18197754 * q^37 + 734520 * q^39 + 9033834 * q^41 + 19594732 * q^43 + 33356142 * q^45 - 18484176 * q^47 - 21483271 * q^49 + 19175880 * q^51 + 10255766 * q^53 - 194217656 * q^55 + 33210960 * q^57 + 121666556 * q^59 - 45948962 * q^61 + 69864552 * q^63 + 25389908 * q^65 + 50535428 * q^67 + 42776160 * q^69 + 267044680 * q^71 - 176213366 * q^73 - 140901060 * q^75 - 406789536 * q^77 - 269685680 * q^79 + 187804089 * q^81 - 227032556 * q^83 + 662846252 * q^85 - 124550280 * q^87 + 72141594 * q^89 + 53179248 * q^91 + 385226880 * q^93 + 1147992184 * q^95 + 228776546 * q^97 - 1506076452 * 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

−60.0000

0

−2074.00

0

−4344.00

0

−16083.0

0

Atkin-Lehner signs

$p$	Sign
$2$	$+1$

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	8.10.a.a	✓	1
3.b	odd	2	1		72.10.a.e		1
4.b	odd	2	1		16.10.a.c		1
5.b	even	2	1		200.10.a.b		1
5.c	odd	4	2		200.10.c.b		2
7.b	odd	2	1		392.10.a.b		1
8.b	even	2	1		64.10.a.f		1
8.d	odd	2	1		64.10.a.d		1
12.b	even	2	1		144.10.a.n		1
16.e	even	4	2		256.10.b.i		2
16.f	odd	4	2		256.10.b.c		2
20.d	odd	2	1		400.10.a.d		1
20.e	even	4	2		400.10.c.g		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
8.10.a.a	✓	1	1.a	even	1	1	trivial
16.10.a.c		1	4.b	odd	2	1
64.10.a.d		1	8.d	odd	2	1
64.10.a.f		1	8.b	even	2	1
72.10.a.e		1	3.b	odd	2	1
144.10.a.n		1	12.b	even	2	1
200.10.a.b		1	5.b	even	2	1
200.10.c.b		2	5.c	odd	4	2
256.10.b.c		2	16.f	odd	4	2
256.10.b.i		2	16.e	even	4	2
392.10.a.b		1	7.b	odd	2	1
400.10.a.d		1	20.d	odd	2	1
400.10.c.g		2	20.e	even	4	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{3} + 60$ acting on $S_{10}^{\mathrm{new}}(\Gamma_0(8))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T + 60$
$5$	$T + 2074$
$7$	$T + 4344$
$11$	$T - 93644$