Newform orbit 2023.1.c.c

• Label: 2023.1.c.c
• Level: $2023$
• Weight: $1$
• Character orbit: 2023.c
• Self dual: yes
• Analytic conductor: $1.010$
• Analytic rank: $0$
• Dimension: $3$
• Projective image: $D_{9}$
• 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:	\(3\)
Coefficient field:	\(\Q(\zeta_{18})^+\)
Defining polynomial:	\( x^{3} - 3x - 1 \)
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	yes
Projective image:	\(D_{9}\)
Projective field:	Galois closure of 9.1.16748793615841.1

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\beta_2\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q - \beta_1 q^{2} + (\beta_{2} + 1) q^{4} - q^{7} + ( - \beta_1 - 1) q^{8} + q^{9}+O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{4} - 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \)

Basis of coefficient ring in terms of \(\nu = \zeta_{18} + \zeta_{18}^{-1}\):

\(\beta_{1}\)	\(=\)	\( \nu \)
\(\beta_{2}\)	\(=\)	\( \nu^{2} - 2 \)

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

1.87939
−0.347296
−1.53209

−1.87939

0

2.53209

0

0

−1.00000

−2.87939

1.00000

0

1735.2

0.347296

0

−0.879385

0

0

−1.00000

−0.652704

1.00000

0

1735.3

1.53209

0

1.34730

0

0

−1.00000

0.532089

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.c	✓	3
7.b	odd	2	1	CM	2023.1.c.c	✓	3
17.b	even	2	1		2023.1.c.d	yes	3
17.c	even	4	2		2023.1.d.b		6
17.d	even	8	4		2023.1.f.c		12
17.e	odd	16	8		2023.1.l.c		24
119.d	odd	2	1		2023.1.c.d	yes	3
119.f	odd	4	2		2023.1.d.b		6
119.l	odd	8	4		2023.1.f.c		12
119.p	even	16	8		2023.1.l.c		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2023.1.c.c	✓	3	1.a	even	1	1	trivial
2023.1.c.c	✓	3	7.b	odd	2	1	CM
2023.1.c.d	yes	3	17.b	even	2	1
2023.1.c.d	yes	3	119.d	odd	2	1
2023.1.d.b		6	17.c	even	4	2
2023.1.d.b		6	119.f	odd	4	2
2023.1.f.c		12	17.d	even	8	4
2023.1.f.c		12	119.l	odd	8	4
2023.1.l.c		24	17.e	odd	16	8
2023.1.l.c		24	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 \(S_{1}^{\mathrm{new}}(2023, [\chi])\):

\( T_{2}^{3} - 3T_{2} + 1 \)

\( T_{11} - 1 \)

Hecke characteristic polynomials

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