Newform orbit 816.2.a.g

• Label: 816.2.a.g
• Level: $816$
• Weight: $2$
• Character orbit: 816.a
• Self dual: yes
• Analytic conductor: $6.516$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$816 = 2^{4} \cdot 3 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	816.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$6.51579280494$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 51)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - q^3 + 3 * q^5 + 4 * q^7 + q^9 + 3 * q^11 - q^13 - 3 * q^15 - q^17 + q^19 - 4 * q^21 - 9 * q^23 + 4 * q^25 - q^27 + 6 * q^29 - 2 * q^31 - 3 * q^33 + 12 * q^35 - 4 * q^37 + q^39 - 3 * q^41 + 7 * q^43 + 3 * q^45 + 6 * q^47 + 9 * q^49 + q^51 - 6 * q^53 + 9 * q^55 - q^57 - 6 * q^59 + 8 * q^61 + 4 * q^63 - 3 * q^65 + 4 * q^67 + 9 * q^69 - 12 * q^71 + 2 * q^73 - 4 * q^75 + 12 * q^77 + 10 * q^79 + q^81 + 6 * q^83 - 3 * q^85 - 6 * q^87 - 4 * q^91 + 2 * q^93 + 3 * q^95 - 16 * q^97 + 3 * 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

−1.00000

0

3.00000

0

4.00000

0

1.00000

0

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$+1$
$17$	$+1$

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	816.2.a.g		1
3.b	odd	2	1		2448.2.a.c		1
4.b	odd	2	1		51.2.a.a	✓	1
8.b	even	2	1		3264.2.a.r		1
8.d	odd	2	1		3264.2.a.a		1
12.b	even	2	1		153.2.a.b		1
20.d	odd	2	1		1275.2.a.d		1
20.e	even	4	2		1275.2.b.b		2
24.f	even	2	1		9792.2.a.by		1
24.h	odd	2	1		9792.2.a.cd		1
28.d	even	2	1		2499.2.a.d		1
44.c	even	2	1		6171.2.a.e		1
52.b	odd	2	1		8619.2.a.g		1
60.h	even	2	1		3825.2.a.i		1
68.d	odd	2	1		867.2.a.c		1
68.f	odd	4	2		867.2.d.a		2
68.g	odd	8	4		867.2.e.e		4
68.i	even	16	8		867.2.h.c		8
84.h	odd	2	1		7497.2.a.j		1
204.h	even	2	1		2601.2.a.f		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
51.2.a.a	✓	1	4.b	odd	2	1
153.2.a.b		1	12.b	even	2	1
816.2.a.g		1	1.a	even	1	1	trivial
867.2.a.c		1	68.d	odd	2	1
867.2.d.a		2	68.f	odd	4	2
867.2.e.e		4	68.g	odd	8	4
867.2.h.c		8	68.i	even	16	8
1275.2.a.d		1	20.d	odd	2	1
1275.2.b.b		2	20.e	even	4	2
2448.2.a.c		1	3.b	odd	2	1
2499.2.a.d		1	28.d	even	2	1
2601.2.a.f		1	204.h	even	2	1
3264.2.a.a		1	8.d	odd	2	1
3264.2.a.r		1	8.b	even	2	1
3825.2.a.i		1	60.h	even	2	1
6171.2.a.e		1	44.c	even	2	1
7497.2.a.j		1	84.h	odd	2	1
8619.2.a.g		1	52.b	odd	2	1
9792.2.a.by		1	24.f	even	2	1
9792.2.a.cd		1	24.h	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(816))$:

$T_{5} - 3$

$T_{7} - 4$

$T_{19} - 1$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T + 1$
$5$	$T - 3$
$7$	$T - 4$
$11$	$T - 3$