Newform orbit 63.6.a.e

• Label: 63.6.a.e
• Level: $63$
• Weight: $6$
• Character orbit: 63.a
• Self dual: yes
• Analytic conductor: $10.104$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$63 = 3^{2} \cdot 7$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	63.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + 10 * q^2 + 68 * q^4 + 56 * q^5 - 49 * q^7 + 360 * q^8 + 560 * q^10 - 232 * q^11 - 140 * q^13 - 490 * q^14 + 1424 * q^16 + 1722 * q^17 - 98 * q^19 + 3808 * q^20 - 2320 * q^22 - 1824 * q^23 + 11 * q^25 - 1400 * q^26 - 3332 * q^28 - 3418 * q^29 - 7644 * q^31 + 2720 * q^32 + 17220 * q^34 - 2744 * q^35 - 10398 * q^37 - 980 * q^38 + 20160 * q^40 + 17962 * q^41 + 10880 * q^43 - 15776 * q^44 - 18240 * q^46 - 9324 * q^47 + 2401 * q^49 + 110 * q^50 - 9520 * q^52 - 2262 * q^53 - 12992 * q^55 - 17640 * q^56 - 34180 * q^58 + 2730 * q^59 + 25648 * q^61 - 76440 * q^62 - 18368 * q^64 - 7840 * q^65 - 48404 * q^67 + 117096 * q^68 - 27440 * q^70 + 58560 * q^71 + 68082 * q^73 - 103980 * q^74 - 6664 * q^76 + 11368 * q^77 + 31784 * q^79 + 79744 * q^80 + 179620 * q^82 + 20538 * q^83 + 96432 * q^85 + 108800 * q^86 - 83520 * q^88 + 50582 * q^89 + 6860 * q^91 - 124032 * q^92 - 93240 * q^94 - 5488 * q^95 - 58506 * q^97 + 24010 * q^98

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

10.0000

0

68.0000

56.0000

0

−49.0000

360.000

0

560.000

Atkin-Lehner signs

$p$	Sign
$3$	$-1$
$7$	$+1$

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	63.6.a.e		1
3.b	odd	2	1		7.6.a.a	✓	1
4.b	odd	2	1		1008.6.a.y		1
7.b	odd	2	1		441.6.a.k		1
12.b	even	2	1		112.6.a.g		1
15.d	odd	2	1		175.6.a.b		1
15.e	even	4	2		175.6.b.a		2
21.c	even	2	1		49.6.a.a		1
21.g	even	6	2		49.6.c.b		2
21.h	odd	6	2		49.6.c.c		2
24.f	even	2	1		448.6.a.c		1
24.h	odd	2	1		448.6.a.m		1
33.d	even	2	1		847.6.a.b		1
84.h	odd	2	1		784.6.a.c		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
7.6.a.a	✓	1	3.b	odd	2	1
49.6.a.a		1	21.c	even	2	1
49.6.c.b		2	21.g	even	6	2
49.6.c.c		2	21.h	odd	6	2
63.6.a.e		1	1.a	even	1	1	trivial
112.6.a.g		1	12.b	even	2	1
175.6.a.b		1	15.d	odd	2	1
175.6.b.a		2	15.e	even	4	2
441.6.a.k		1	7.b	odd	2	1
448.6.a.c		1	24.f	even	2	1
448.6.a.m		1	24.h	odd	2	1
784.6.a.c		1	84.h	odd	2	1
847.6.a.b		1	33.d	even	2	1
1008.6.a.y		1	4.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2} - 10$ acting on $S_{6}^{\mathrm{new}}(\Gamma_0(63))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T - 10$
$3$	$T$
$5$	$T - 56$
$7$	$T + 49$
$11$	$T + 232$