Properties

Label 83.1.b.a
Level 83
Weight 1
Character orbit 83.b
Self dual yes
Analytic conductor 0.041
Analytic rank 0
Dimension 1
Projective image \(D_{3}\)
CM discriminant -83
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 83 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 83.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.0414223960485\)
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 3.1.83.1
Artin image $S_3$
Artin field Galois closure of 3.1.83.1

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} + q^{4} - q^{7} + O(q^{10}) \) \( q - q^{3} + q^{4} - q^{7} - q^{11} - q^{12} + q^{16} - q^{17} + q^{21} + 2q^{23} + q^{25} + q^{27} - q^{28} - q^{29} - q^{31} + q^{33} - q^{37} + 2q^{41} - q^{44} - q^{48} + q^{51} - q^{59} - q^{61} + q^{64} - q^{68} - 2q^{69} - q^{75} + q^{77} - q^{81} + q^{83} + q^{84} + q^{87} + 2q^{92} + q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/83\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
82.1
0
0 −1.00000 1.00000 0 0 −1.00000 0 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
83.b odd 2 1 CM by \(\Q(\sqrt{-83}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 83.1.b.a 1
3.b odd 2 1 747.1.c.a 1
4.b odd 2 1 1328.1.g.a 1
5.b even 2 1 2075.1.c.f 1
5.c odd 4 2 2075.1.d.c 2
83.b odd 2 1 CM 83.1.b.a 1
249.d even 2 1 747.1.c.a 1
332.b even 2 1 1328.1.g.a 1
415.d odd 2 1 2075.1.c.f 1
415.e even 4 2 2075.1.d.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
83.1.b.a 1 1.a even 1 1 trivial
83.1.b.a 1 83.b odd 2 1 CM
747.1.c.a 1 3.b odd 2 1
747.1.c.a 1 249.d even 2 1
1328.1.g.a 1 4.b odd 2 1
1328.1.g.a 1 332.b even 2 1
2075.1.c.f 1 5.b even 2 1
2075.1.c.f 1 415.d odd 2 1
2075.1.d.c 2 5.c odd 4 2
2075.1.d.c 2 415.e even 4 2

Hecke kernels

This newform subspace is the entire newspace \(S_{1}^{\mathrm{new}}(83, [\chi])\).

Hecke characteristic polynomials

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