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

$q$-expansion

\(f(q)\)

\(=\)

\( q - q^{5} - q^{7} + q^{9}+O(q^{10}) \)

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

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