Newform orbit 2023.1.c.a

• Label: 2023.1.c.a
• Level: $2023$
• Weight: $1$
• Character orbit: 2023.c
• Self dual: yes
• Analytic conductor: $1.010$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -7
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2023 = 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2023.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(1.00960852056\)
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 3.1.2023.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.69572993.1

$q$-expansion

\(f(q)\)

\(=\)

\( q - q^{2} - q^{7} + q^{8} + q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2023\mathbb{Z}\right)^\times\).

\(n\)	\(290\)	\(1737\)
\(\chi(n)\)	\(-1\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1735.1

0

−1.00000

0

0

0

0

−1.00000

1.00000

1.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.b	odd	2	1	CM by \(\Q(\sqrt{-7}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2023.1.c.a	✓	1
7.b	odd	2	1	CM	2023.1.c.a	✓	1
17.b	even	2	1		2023.1.c.b	yes	1
17.c	even	4	2		2023.1.d.a		2
17.d	even	8	4		2023.1.f.a		4
17.e	odd	16	8		2023.1.l.a		8
119.d	odd	2	1		2023.1.c.b	yes	1
119.f	odd	4	2		2023.1.d.a		2
119.l	odd	8	4		2023.1.f.a		4
119.p	even	16	8		2023.1.l.a		8

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2023.1.c.a	✓	1	1.a	even	1	1	trivial
2023.1.c.a	✓	1	7.b	odd	2	1	CM
2023.1.c.b	yes	1	17.b	even	2	1
2023.1.c.b	yes	1	119.d	odd	2	1
2023.1.d.a		2	17.c	even	4	2
2023.1.d.a		2	119.f	odd	4	2
2023.1.f.a		4	17.d	even	8	4
2023.1.f.a		4	119.l	odd	8	4
2023.1.l.a		8	17.e	odd	16	8
2023.1.l.a		8	119.p	even	16	8

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(2023, [\chi])\):

\( T_{2} + 1 \)

\( T_{11} + 2 \)

Hecke characteristic polynomials

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