Newform orbit 2156.1.h.a

• Label: 2156.1.h.a
• Level: $2156$
• Weight: $1$
• Character orbit: 2156.h
• Self dual: yes
• Analytic conductor: $1.076$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -11
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2156.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(1.07598416724\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 44)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.44.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.664048.1

$q$-expansion

\(f(q)\)

\(=\)

\( q + q^{3} + q^{5}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2156\mathbb{Z}\right)^\times\).

\(n\)	\(981\)	\(1079\)	\(1277\)
\(\chi(n)\)	\(1\)	\(0\)	\(0\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

197.1

0

0

1.00000

0

1.00000

0

0

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	CM by \(\Q(\sqrt{-11}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2156.1.h.a		1
7.b	odd	2	1		44.1.d.a	✓	1
7.c	even	3	2		2156.1.k.a		2
7.d	odd	6	2		2156.1.k.b		2
11.b	odd	2	1	CM	2156.1.h.a		1
21.c	even	2	1		396.1.f.a		1
28.d	even	2	1		176.1.h.a		1
35.c	odd	2	1		1100.1.f.a		1
35.f	even	4	2		1100.1.e.a		2
56.e	even	2	1		704.1.h.a		1
56.h	odd	2	1		704.1.h.b		1
63.l	odd	6	2		3564.1.m.b		2
63.o	even	6	2		3564.1.m.a		2
77.b	even	2	1		44.1.d.a	✓	1
77.h	odd	6	2		2156.1.k.a		2
77.i	even	6	2		2156.1.k.b		2
77.j	odd	10	4		484.1.f.a		4
77.l	even	10	4		484.1.f.a		4
84.h	odd	2	1		1584.1.j.a		1
112.j	even	4	2		2816.1.b.a		2
112.l	odd	4	2		2816.1.b.b		2
231.h	odd	2	1		396.1.f.a		1
308.g	odd	2	1		176.1.h.a		1
308.s	odd	10	4		1936.1.n.a		4
308.t	even	10	4		1936.1.n.a		4
385.h	even	2	1		1100.1.f.a		1
385.l	odd	4	2		1100.1.e.a		2
616.g	odd	2	1		704.1.h.a		1
616.o	even	2	1		704.1.h.b		1
693.u	odd	6	2		3564.1.m.a		2
693.bj	even	6	2		3564.1.m.b		2
924.n	even	2	1		1584.1.j.a		1
1232.u	odd	4	2		2816.1.b.a		2
1232.x	even	4	2		2816.1.b.b		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
44.1.d.a	✓	1	7.b	odd	2	1
44.1.d.a	✓	1	77.b	even	2	1
176.1.h.a		1	28.d	even	2	1
176.1.h.a		1	308.g	odd	2	1
396.1.f.a		1	21.c	even	2	1
396.1.f.a		1	231.h	odd	2	1
484.1.f.a		4	77.j	odd	10	4
484.1.f.a		4	77.l	even	10	4
704.1.h.a		1	56.e	even	2	1
704.1.h.a		1	616.g	odd	2	1
704.1.h.b		1	56.h	odd	2	1
704.1.h.b		1	616.o	even	2	1
1100.1.e.a		2	35.f	even	4	2
1100.1.e.a		2	385.l	odd	4	2
1100.1.f.a		1	35.c	odd	2	1
1100.1.f.a		1	385.h	even	2	1
1584.1.j.a		1	84.h	odd	2	1
1584.1.j.a		1	924.n	even	2	1
1936.1.n.a		4	308.s	odd	10	4
1936.1.n.a		4	308.t	even	10	4
2156.1.h.a		1	1.a	even	1	1	trivial
2156.1.h.a		1	11.b	odd	2	1	CM
2156.1.k.a		2	7.c	even	3	2
2156.1.k.a		2	77.h	odd	6	2
2156.1.k.b		2	7.d	odd	6	2
2156.1.k.b		2	77.i	even	6	2
2816.1.b.a		2	112.j	even	4	2
2816.1.b.a		2	1232.u	odd	4	2
2816.1.b.b		2	112.l	odd	4	2
2816.1.b.b		2	1232.x	even	4	2
3564.1.m.a		2	63.o	even	6	2
3564.1.m.a		2	693.u	odd	6	2
3564.1.m.b		2	63.l	odd	6	2
3564.1.m.b		2	693.bj	even	6	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 1 \) acting on \(S_{1}^{\mathrm{new}}(2156, [\chi])\).

Hecke characteristic polynomials

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