Properties

Label 83.2.a.a
Level $83$
Weight $2$
Character orbit 83.a
Self dual yes
Analytic conductor $0.663$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 83 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 83.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(0.662758336777\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} - 2 q^{9} + 2 q^{10} + 3 q^{11} + q^{12} - 6 q^{13} + 3 q^{14} + 2 q^{15} - q^{16} + 5 q^{17} + 2 q^{18} + 2 q^{19} + 2 q^{20} + 3 q^{21} - 3 q^{22} - 4 q^{23} - 3 q^{24} - q^{25} + 6 q^{26} + 5 q^{27} + 3 q^{28} - 7 q^{29} - 2 q^{30} + 5 q^{31} - 5 q^{32} - 3 q^{33} - 5 q^{34} + 6 q^{35} + 2 q^{36} - 11 q^{37} - 2 q^{38} + 6 q^{39} - 6 q^{40} - 2 q^{41} - 3 q^{42} - 8 q^{43} - 3 q^{44} + 4 q^{45} + 4 q^{46} + q^{48} + 2 q^{49} + q^{50} - 5 q^{51} + 6 q^{52} + 6 q^{53} - 5 q^{54} - 6 q^{55} - 9 q^{56} - 2 q^{57} + 7 q^{58} + 5 q^{59} - 2 q^{60} + 5 q^{61} - 5 q^{62} + 6 q^{63} + 7 q^{64} + 12 q^{65} + 3 q^{66} - 2 q^{67} - 5 q^{68} + 4 q^{69} - 6 q^{70} + 2 q^{71} - 6 q^{72} + 11 q^{74} + q^{75} - 2 q^{76} - 9 q^{77} - 6 q^{78} + 14 q^{79} + 2 q^{80} + q^{81} + 2 q^{82} - q^{83} - 3 q^{84} - 10 q^{85} + 8 q^{86} + 7 q^{87} + 9 q^{88} - 4 q^{90} + 18 q^{91} + 4 q^{92} - 5 q^{93} - 4 q^{95} + 5 q^{96} - 8 q^{97} - 2 q^{98} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
−1.00000 −1.00000 −1.00000 −2.00000 1.00000 −3.00000 3.00000 −2.00000 2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(83\) \(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 83.2.a.a 1
3.b odd 2 1 747.2.a.d 1
4.b odd 2 1 1328.2.a.c 1
5.b even 2 1 2075.2.a.d 1
7.b odd 2 1 4067.2.a.a 1
8.b even 2 1 5312.2.a.l 1
8.d odd 2 1 5312.2.a.h 1
83.b odd 2 1 6889.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
83.2.a.a 1 1.a even 1 1 trivial
747.2.a.d 1 3.b odd 2 1
1328.2.a.c 1 4.b odd 2 1
2075.2.a.d 1 5.b even 2 1
4067.2.a.a 1 7.b odd 2 1
5312.2.a.h 1 8.d odd 2 1
5312.2.a.l 1 8.b even 2 1
6889.2.a.a 1 83.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} + 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(83))\). 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
$5$ \( T + 2 \) Copy content Toggle raw display
$7$ \( T + 3 \) Copy content Toggle raw display
$11$ \( T - 3 \) Copy content Toggle raw display
$13$ \( T + 6 \) Copy content Toggle raw display
$17$ \( T - 5 \) Copy content Toggle raw display
$19$ \( T - 2 \) Copy content Toggle raw display
$23$ \( T + 4 \) Copy content Toggle raw display
$29$ \( T + 7 \) Copy content Toggle raw display
$31$ \( T - 5 \) Copy content Toggle raw display
$37$ \( T + 11 \) Copy content Toggle raw display
$41$ \( T + 2 \) Copy content Toggle raw display
$43$ \( T + 8 \) Copy content Toggle raw display
$47$ \( T \) Copy content Toggle raw display
$53$ \( T - 6 \) Copy content Toggle raw display
$59$ \( T - 5 \) Copy content Toggle raw display
$61$ \( T - 5 \) Copy content Toggle raw display
$67$ \( T + 2 \) Copy content Toggle raw display
$71$ \( T - 2 \) Copy content Toggle raw display
$73$ \( T \) Copy content Toggle raw display
$79$ \( T - 14 \) Copy content Toggle raw display
$83$ \( T + 1 \) Copy content Toggle raw display
$89$ \( T \) Copy content Toggle raw display
$97$ \( T + 8 \) Copy content Toggle raw display
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