Newform orbit 1216.3.e.b

• Label: 1216.3.e.b
• Level: $1216$
• Weight: $3$
• Character orbit: 1216.e
• Self dual: yes
• Analytic conductor: $33.134$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -19
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$1216 = 2^{6} \cdot 19$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	1216.e (of order $2$, degree $1$, not minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$33.1336001462$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

$f(q)$

$=$

q + 9 * q^5 + 5 * q^7 + 9 * q^9 + 3 * q^11 + 15 * q^17 - 19 * q^19 + 30 * q^23 + 56 * q^25 + 45 * q^35 - 85 * q^43 + 81 * q^45 - 75 * q^47 - 24 * q^49 + 27 * q^55 - 103 * q^61 + 45 * q^63 - 25 * q^73 + 15 * q^77 + 81 * q^81 + 90 * q^83 + 135 * q^85 - 171 * q^95 + 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$-1$	$1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

1025.1

0

0

0

0

9.00000

0

5.00000

0

9.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
19.b	odd	2	1	CM by $\Q(\sqrt{-19})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1216.3.e.b		1
4.b	odd	2	1		1216.3.e.a		1
8.b	even	2	1		304.3.e.a		1
8.d	odd	2	1		19.3.b.a	✓	1
19.b	odd	2	1	CM	1216.3.e.b		1
24.f	even	2	1		171.3.c.a		1
24.h	odd	2	1		2736.3.o.a		1
40.e	odd	2	1		475.3.c.a		1
40.k	even	4	2		475.3.d.a		2
76.d	even	2	1		1216.3.e.a		1
152.b	even	2	1		19.3.b.a	✓	1
152.g	odd	2	1		304.3.e.a		1
152.k	odd	6	2		361.3.d.a		2
152.o	even	6	2		361.3.d.a		2
152.u	odd	18	6		361.3.f.a		6
152.v	even	18	6		361.3.f.a		6
456.l	odd	2	1		171.3.c.a		1
456.p	even	2	1		2736.3.o.a		1
760.p	even	2	1		475.3.c.a		1
760.y	odd	4	2		475.3.d.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
19.3.b.a	✓	1	8.d	odd	2	1
19.3.b.a	✓	1	152.b	even	2	1
171.3.c.a		1	24.f	even	2	1
171.3.c.a		1	456.l	odd	2	1
304.3.e.a		1	8.b	even	2	1
304.3.e.a		1	152.g	odd	2	1
361.3.d.a		2	152.k	odd	6	2
361.3.d.a		2	152.o	even	6	2
361.3.f.a		6	152.u	odd	18	6
361.3.f.a		6	152.v	even	18	6
475.3.c.a		1	40.e	odd	2	1
475.3.c.a		1	760.p	even	2	1
475.3.d.a		2	40.k	even	4	2
475.3.d.a		2	760.y	odd	4	2
1216.3.e.a		1	4.b	odd	2	1
1216.3.e.a		1	76.d	even	2	1
1216.3.e.b		1	1.a	even	1	1	trivial
1216.3.e.b		1	19.b	odd	2	1	CM
2736.3.o.a		1	24.h	odd	2	1
2736.3.o.a		1	456.p	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{3}^{\mathrm{new}}(1216, [\chi])$:

$T_{3}$

$T_{5} - 9$

$T_{7} - 5$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T - 9$
$7$	$T - 5$
$11$	$T - 3$