Properties

Label 983.1.b.a
Level $983$
Weight $1$
Character orbit 983.b
Self dual yes
Analytic conductor $0.491$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -983
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 983 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 983.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.490580907418\)
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 3.1.983.1
Artin image: $S_3$
Artin field: Galois closure of 3.1.983.1

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{6} - q^{7} + q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} - q^{3} + q^{6} - q^{7} + q^{8} + q^{14} - q^{16} - q^{19} + q^{21} - q^{23} - q^{24} + q^{25} + q^{27} + 2 q^{31} + 2 q^{37} + q^{38} + 2 q^{41} - q^{42} - q^{43} + q^{46} - q^{47} + q^{48} - q^{50} - q^{53} - q^{54} - q^{56} + q^{57} + 2 q^{59} - 2 q^{62} + q^{64} + 2 q^{67} + q^{69} - 2 q^{74} - q^{75} + 2 q^{79} - q^{81} - 2 q^{82} + q^{86} - q^{89} - 2 q^{93} + q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/983\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
982.1
0
−1.00000 −1.00000 0 0 1.00000 −1.00000 1.00000 0 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
983.b odd 2 1 CM by \(\Q(\sqrt{-983}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 983.1.b.a 1
983.b odd 2 1 CM 983.1.b.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
983.1.b.a 1 1.a even 1 1 trivial
983.1.b.a 1 983.b odd 2 1 CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} + 1 \) acting on \(S_{1}^{\mathrm{new}}(983, [\chi])\). Copy content Toggle raw display

Hecke characteristic polynomials

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