Properties

Label 83.7.b.a
Level $83$
Weight $7$
Character orbit 83.b
Self dual yes
Analytic conductor $19.094$
Analytic rank $0$
Dimension $1$
CM discriminant -83
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 83 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 83.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(19.0944889404\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\) \(=\) \( q - 29 q^{3} + 64 q^{4} - 61 q^{7} + 112 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 29 q^{3} + 64 q^{4} - 61 q^{7} + 112 q^{9} + 587 q^{11} - 1856 q^{12} + 4096 q^{16} - 4201 q^{17} + 1769 q^{21} + 8066 q^{23} + 15625 q^{25} + 17893 q^{27} - 3904 q^{28} + 46703 q^{29} + 40907 q^{31} - 17023 q^{33} + 7168 q^{36} + 10919 q^{37} + 5042 q^{41} + 37568 q^{44} - 118784 q^{48} - 113928 q^{49} + 121829 q^{51} - 188917 q^{59} + 435287 q^{61} - 6832 q^{63} + 262144 q^{64} - 268864 q^{68} - 233914 q^{69} - 453125 q^{75} - 35807 q^{77} - 600545 q^{81} - 571787 q^{83} + 113216 q^{84} - 1354387 q^{87} + 516224 q^{92} - 1186303 q^{93} + 65744 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −29.0000 64.0000 0 0 −61.0000 0 112.000 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 83.7.b.a 1
83.b odd 2 1 CM 83.7.b.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
83.7.b.a 1 1.a even 1 1 trivial
83.7.b.a 1 83.b odd 2 1 CM

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{7}^{\mathrm{new}}(83, [\chi])\):

\( T_{2} \) Copy content Toggle raw display
\( T_{3} + 29 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T + 29 \) Copy content Toggle raw display
$5$ \( T \) Copy content Toggle raw display
$7$ \( T + 61 \) Copy content Toggle raw display
$11$ \( T - 587 \) Copy content Toggle raw display
$13$ \( T \) Copy content Toggle raw display
$17$ \( T + 4201 \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T - 8066 \) Copy content Toggle raw display
$29$ \( T - 46703 \) Copy content Toggle raw display
$31$ \( T - 40907 \) Copy content Toggle raw display
$37$ \( T - 10919 \) Copy content Toggle raw display
$41$ \( T - 5042 \) Copy content Toggle raw display
$43$ \( T \) Copy content Toggle raw display
$47$ \( T \) Copy content Toggle raw display
$53$ \( T \) Copy content Toggle raw display
$59$ \( T + 188917 \) Copy content Toggle raw display
$61$ \( T - 435287 \) Copy content Toggle raw display
$67$ \( T \) Copy content Toggle raw display
$71$ \( T \) Copy content Toggle raw display
$73$ \( T \) Copy content Toggle raw display
$79$ \( T \) Copy content Toggle raw display
$83$ \( T + 571787 \) Copy content Toggle raw display
$89$ \( T \) Copy content Toggle raw display
$97$ \( T \) Copy content Toggle raw display
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