Newform orbit 2736.1.o.b

• Label: 2736.1.o.b
• Level: $2736$
• Weight: $1$
• Character orbit: 2736.o
• Self dual: yes
• Analytic conductor: $1.365$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -19
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$2736 = 2^{4} \cdot 3^{2} \cdot 19$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	2736.o (of order $2$, degree $1$, not minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 76)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.76.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.2495232.1
Stark unit:	Root of $x^{6} - 60054x^{5} + 23219151x^{4} - 3560164724x^{3} + 23219151x^{2} - 60054x + 1$

$q$-expansion

$f(q)$

$=$

$q + q^{5} + q^{7} - q^{11} + q^{17} - q^{19} + 2 q^{23} + q^{35} + q^{43} - q^{47} - q^{55} - q^{61} - q^{73} - q^{77} + 2 q^{83} + q^{85} - q^{95}+O(q^{100})$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times$.

$n$	$1009$	$1217$	$1711$	$2053$
$\chi(n)$	$-1$	$1$	$1$	$1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

721.1

0

0

0

0

1.00000

0

1.00000

0

0

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	2736.1.o.b		1
3.b	odd	2	1		304.1.e.a		1
4.b	odd	2	1		684.1.h.a		1
12.b	even	2	1		76.1.c.a	✓	1
19.b	odd	2	1	CM	2736.1.o.b		1
24.f	even	2	1		1216.1.e.a		1
24.h	odd	2	1		1216.1.e.b		1
57.d	even	2	1		304.1.e.a		1
60.h	even	2	1		1900.1.e.a		1
60.l	odd	4	2		1900.1.g.a		2
76.d	even	2	1		684.1.h.a		1
84.h	odd	2	1		3724.1.e.c		1
84.j	odd	6	2		3724.1.bc.b		2
84.n	even	6	2		3724.1.bc.c		2
228.b	odd	2	1		76.1.c.a	✓	1
228.m	even	6	2		1444.1.h.a		2
228.n	odd	6	2		1444.1.h.a		2
228.u	odd	18	6		1444.1.j.a		6
228.v	even	18	6		1444.1.j.a		6
456.l	odd	2	1		1216.1.e.a		1
456.p	even	2	1		1216.1.e.b		1
1140.p	odd	2	1		1900.1.e.a		1
1140.w	even	4	2		1900.1.g.a		2
1596.p	even	2	1		3724.1.e.c		1
1596.bl	even	6	2		3724.1.bc.b		2
1596.cb	odd	6	2		3724.1.bc.c		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
76.1.c.a	✓	1	12.b	even	2	1
76.1.c.a	✓	1	228.b	odd	2	1
304.1.e.a		1	3.b	odd	2	1
304.1.e.a		1	57.d	even	2	1
684.1.h.a		1	4.b	odd	2	1
684.1.h.a		1	76.d	even	2	1
1216.1.e.a		1	24.f	even	2	1
1216.1.e.a		1	456.l	odd	2	1
1216.1.e.b		1	24.h	odd	2	1
1216.1.e.b		1	456.p	even	2	1
1444.1.h.a		2	228.m	even	6	2
1444.1.h.a		2	228.n	odd	6	2
1444.1.j.a		6	228.u	odd	18	6
1444.1.j.a		6	228.v	even	18	6
1900.1.e.a		1	60.h	even	2	1
1900.1.e.a		1	1140.p	odd	2	1
1900.1.g.a		2	60.l	odd	4	2
1900.1.g.a		2	1140.w	even	4	2
2736.1.o.b		1	1.a	even	1	1	trivial
2736.1.o.b		1	19.b	odd	2	1	CM
3724.1.e.c		1	84.h	odd	2	1
3724.1.e.c		1	1596.p	even	2	1
3724.1.bc.b		2	84.j	odd	6	2
3724.1.bc.b		2	1596.bl	even	6	2
3724.1.bc.c		2	84.n	even	6	2
3724.1.bc.c		2	1596.cb	odd	6	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{5} - 1$ acting on $S_{1}^{\mathrm{new}}(2736, [\chi])$.

Hecke characteristic polynomials

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