Newform orbit 676.1.c.a

• Label: 676.1.c.a
• Level: $676$
• Weight: $1$
• Character orbit: 676.c
• Self dual: yes
• Analytic conductor: $0.337$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -4
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	676.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.337367948540\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 52)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.676.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.5940688.1

$q$-expansion

\(f(q)\)

\(=\)

\( q - q^{2} + q^{4} + q^{5} - q^{8} + q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/676\mathbb{Z}\right)^\times\).

\(n\)	\(339\)	\(509\)
\(\chi(n)\)	\(-1\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

339.1

0

−1.00000

0

1.00000

1.00000

0

0

−1.00000

1.00000

−1.00000

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	676.1.c.a		1
4.b	odd	2	1	CM	676.1.c.a		1
13.b	even	2	1		676.1.c.b		1
13.c	even	3	2		676.1.j.a		2
13.d	odd	4	2		676.1.b.a		2
13.e	even	6	2		52.1.j.a	✓	2
13.f	odd	12	4		676.1.i.a		4
39.h	odd	6	2		468.1.br.a		2
52.b	odd	2	1		676.1.c.b		1
52.f	even	4	2		676.1.b.a		2
52.i	odd	6	2		52.1.j.a	✓	2
52.j	odd	6	2		676.1.j.a		2
52.l	even	12	4		676.1.i.a		4
65.l	even	6	2		1300.1.bc.a		2
65.r	odd	12	4		1300.1.w.a		4
91.k	even	6	2		2548.1.bi.b		2
91.l	odd	6	2		2548.1.bi.a		2
91.p	odd	6	2		2548.1.q.a		2
91.t	odd	6	2		2548.1.bn.a		2
91.u	even	6	2		2548.1.q.b		2
104.p	odd	6	2		832.1.bb.a		2
104.s	even	6	2		832.1.bb.a		2
156.r	even	6	2		468.1.br.a		2
208.bh	even	12	4		3328.1.v.b		4
208.bi	odd	12	4		3328.1.v.b		4
260.w	odd	6	2		1300.1.bc.a		2
260.bg	even	12	4		1300.1.w.a		4
364.s	odd	6	2		2548.1.q.b		2
364.w	even	6	2		2548.1.bi.a		2
364.bc	even	6	2		2548.1.bn.a		2
364.bk	odd	6	2		2548.1.bi.b		2
364.bp	even	6	2		2548.1.q.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
52.1.j.a	✓	2	13.e	even	6	2
52.1.j.a	✓	2	52.i	odd	6	2
468.1.br.a		2	39.h	odd	6	2
468.1.br.a		2	156.r	even	6	2
676.1.b.a		2	13.d	odd	4	2
676.1.b.a		2	52.f	even	4	2
676.1.c.a		1	1.a	even	1	1	trivial
676.1.c.a		1	4.b	odd	2	1	CM
676.1.c.b		1	13.b	even	2	1
676.1.c.b		1	52.b	odd	2	1
676.1.i.a		4	13.f	odd	12	4
676.1.i.a		4	52.l	even	12	4
676.1.j.a		2	13.c	even	3	2
676.1.j.a		2	52.j	odd	6	2
832.1.bb.a		2	104.p	odd	6	2
832.1.bb.a		2	104.s	even	6	2
1300.1.w.a		4	65.r	odd	12	4
1300.1.w.a		4	260.bg	even	12	4
1300.1.bc.a		2	65.l	even	6	2
1300.1.bc.a		2	260.w	odd	6	2
2548.1.q.a		2	91.p	odd	6	2
2548.1.q.a		2	364.bp	even	6	2
2548.1.q.b		2	91.u	even	6	2
2548.1.q.b		2	364.s	odd	6	2
2548.1.bi.a		2	91.l	odd	6	2
2548.1.bi.a		2	364.w	even	6	2
2548.1.bi.b		2	91.k	even	6	2
2548.1.bi.b		2	364.bk	odd	6	2
2548.1.bn.a		2	91.t	odd	6	2
2548.1.bn.a		2	364.bc	even	6	2
3328.1.v.b		4	208.bh	even	12	4
3328.1.v.b		4	208.bi	odd	12	4

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} - 1 \) acting on \(S_{1}^{\mathrm{new}}(676, [\chi])\).

Hecke characteristic polynomials

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