Properties

Label 2023.1.c.b
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 $2$

Related objects

Downloads

Learn more

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: $S_3$
Artin field: Galois closure of 3.1.2023.1

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{7} + q^{8} + q^{9} + 2q^{11} - q^{14} - q^{16} - q^{18} - 2q^{22} - q^{23} + q^{25} - q^{29} - q^{37} - q^{43} + q^{46} + q^{49} - q^{50} - q^{53} + q^{56} + q^{58} + q^{63} + q^{64} + 2q^{67} - q^{71} + q^{72} + q^{74} + 2q^{77} - q^{79} + q^{81} + q^{86} + 2q^{88} - q^{98} + 2q^{99} + O(q^{100}) \)

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
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

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.b yes 1
7.b odd 2 1 CM 2023.1.c.b yes 1
17.b even 2 1 2023.1.c.a 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.a 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 17.b even 2 1
2023.1.c.a 1 119.d odd 2 1
2023.1.c.b yes 1 1.a even 1 1 trivial
2023.1.c.b yes 1 7.b odd 2 1 CM
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

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( -1 + T \)
$11$ \( -2 + T \)
$13$ \( T \)
$17$ \( T \)
$19$ \( T \)
$23$ \( 1 + T \)
$29$ \( 1 + T \)
$31$ \( T \)
$37$ \( 1 + T \)
$41$ \( T \)
$43$ \( 1 + T \)
$47$ \( T \)
$53$ \( 1 + T \)
$59$ \( T \)
$61$ \( T \)
$67$ \( -2 + T \)
$71$ \( 1 + T \)
$73$ \( T \)
$79$ \( 1 + T \)
$83$ \( T \)
$89$ \( T \)
$97$ \( T \)
show more
show less