Newform orbit 256.3.c.a

• Label: 256.3.c.a
• Level: $256$
• Weight: $3$
• Character orbit: 256.c
• Self dual: yes
• Analytic conductor: $6.975$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -4
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$256 = 2^{8}$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	256.c (of order $2$, degree $1$, not minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$6.97549476762$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

$f(q)$

$=$

q - 8 * q^5 + 9 * q^9 + 24 * q^13 + 30 * q^17 + 39 * q^25 - 40 * q^29 + 24 * q^37 - 18 * q^41 - 72 * q^45 + 49 * q^49 + 56 * q^53 + 120 * q^61 - 192 * q^65 - 110 * q^73 + 81 * q^81 - 240 * q^85 - 78 * q^89 - 130 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$1$	$-1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

255.1

0

0

0

0

−8.00000

0

0

0

9.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	CM by $\Q(\sqrt{-1})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	256.3.c.a		1
3.b	odd	2	1		2304.3.g.f		1
4.b	odd	2	1	CM	256.3.c.a		1
8.b	even	2	1		256.3.c.b		1
8.d	odd	2	1		256.3.c.b		1
12.b	even	2	1		2304.3.g.f		1
16.e	even	4	2		128.3.d.a	✓	2
16.f	odd	4	2		128.3.d.a	✓	2
24.f	even	2	1		2304.3.g.a		1
24.h	odd	2	1		2304.3.g.a		1
48.i	odd	4	2		1152.3.b.a		2
48.k	even	4	2		1152.3.b.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
128.3.d.a	✓	2	16.e	even	4	2
128.3.d.a	✓	2	16.f	odd	4	2
256.3.c.a		1	1.a	even	1	1	trivial
256.3.c.a		1	4.b	odd	2	1	CM
256.3.c.b		1	8.b	even	2	1
256.3.c.b		1	8.d	odd	2	1
1152.3.b.a		2	48.i	odd	4	2
1152.3.b.a		2	48.k	even	4	2
2304.3.g.a		1	24.f	even	2	1
2304.3.g.a		1	24.h	odd	2	1
2304.3.g.f		1	3.b	odd	2	1
2304.3.g.f		1	12.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{3}^{\mathrm{new}}(256, [\chi])$:

$T_{3}$

$T_{5} + 8$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T + 8$
$7$	$T$
$11$	$T$