Newform orbit 76.1.c.a

• Label: 76.1.c.a
• Level: $76$
• Weight: $1$
• Character orbit: 76.c
• Self dual: yes
• Analytic conductor: $0.038$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -19
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$76 = 2^{2} \cdot 19$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	76.c (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$0.0379289409601$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.76.1
Artin image:	$S_3$
Artin field:	Galois closure of 3.1.76.1
Stark unit:	Root of $x^{3} - 3x^{2} + x - 1$

$q$-expansion

$f(q)$

$=$

q - q^5 - q^7 + q^9 - q^11 - q^17 + q^19 + 2 * q^23 + q^35 - q^43 - q^45 - q^47 + q^55 - q^61 - q^63 - q^73 + q^77 + q^81 + 2 * q^83 + q^85 - q^95 - q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$-1$	$1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

37.1

0

0

0

0

−1.00000

0

−1.00000

0

1.00000

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	76.1.c.a	✓	1
3.b	odd	2	1		684.1.h.a		1
4.b	odd	2	1		304.1.e.a		1
5.b	even	2	1		1900.1.e.a		1
5.c	odd	4	2		1900.1.g.a		2
7.b	odd	2	1		3724.1.e.c		1
7.c	even	3	2		3724.1.bc.c		2
7.d	odd	6	2		3724.1.bc.b		2
8.b	even	2	1		1216.1.e.a		1
8.d	odd	2	1		1216.1.e.b		1
12.b	even	2	1		2736.1.o.b		1
19.b	odd	2	1	CM	76.1.c.a	✓	1
19.c	even	3	2		1444.1.h.a		2
19.d	odd	6	2		1444.1.h.a		2
19.e	even	9	6		1444.1.j.a		6
19.f	odd	18	6		1444.1.j.a		6
57.d	even	2	1		684.1.h.a		1
76.d	even	2	1		304.1.e.a		1
95.d	odd	2	1		1900.1.e.a		1
95.g	even	4	2		1900.1.g.a		2
133.c	even	2	1		3724.1.e.c		1
133.o	even	6	2		3724.1.bc.b		2
133.r	odd	6	2		3724.1.bc.c		2
152.b	even	2	1		1216.1.e.b		1
152.g	odd	2	1		1216.1.e.a		1
228.b	odd	2	1		2736.1.o.b		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
76.1.c.a	✓	1	1.a	even	1	1	trivial
76.1.c.a	✓	1	19.b	odd	2	1	CM
304.1.e.a		1	4.b	odd	2	1
304.1.e.a		1	76.d	even	2	1
684.1.h.a		1	3.b	odd	2	1
684.1.h.a		1	57.d	even	2	1
1216.1.e.a		1	8.b	even	2	1
1216.1.e.a		1	152.g	odd	2	1
1216.1.e.b		1	8.d	odd	2	1
1216.1.e.b		1	152.b	even	2	1
1444.1.h.a		2	19.c	even	3	2
1444.1.h.a		2	19.d	odd	6	2
1444.1.j.a		6	19.e	even	9	6
1444.1.j.a		6	19.f	odd	18	6
1900.1.e.a		1	5.b	even	2	1
1900.1.e.a		1	95.d	odd	2	1
1900.1.g.a		2	5.c	odd	4	2
1900.1.g.a		2	95.g	even	4	2
2736.1.o.b		1	12.b	even	2	1
2736.1.o.b		1	228.b	odd	2	1
3724.1.e.c		1	7.b	odd	2	1
3724.1.e.c		1	133.c	even	2	1
3724.1.bc.b		2	7.d	odd	6	2
3724.1.bc.b		2	133.o	even	6	2
3724.1.bc.c		2	7.c	even	3	2
3724.1.bc.c		2	133.r	odd	6	2

Hecke kernels

This newform subspace is the entire newspace $S_{1}^{\mathrm{new}}(76, [\chi])$.

Hecke characteristic polynomials

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