Properties

Label 5082.2.a.s
Level $5082$
Weight $2$
Character orbit 5082.a
Self dual yes
Analytic conductor $40.580$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5082 = 2 \cdot 3 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5082.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(40.5799743072\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 462)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} + q^{9} - q^{12} + 2 q^{13} + q^{14} + q^{16} + 4 q^{17} + q^{18} - 6 q^{19} - q^{21} - 4 q^{23} - q^{24} - 5 q^{25} + 2 q^{26} - q^{27} + q^{28} + 10 q^{29} + 6 q^{31} + q^{32} + 4 q^{34} + q^{36} - 6 q^{37} - 6 q^{38} - 2 q^{39} + 12 q^{41} - q^{42} + 8 q^{43} - 4 q^{46} + 2 q^{47} - q^{48} + q^{49} - 5 q^{50} - 4 q^{51} + 2 q^{52} + 6 q^{53} - q^{54} + q^{56} + 6 q^{57} + 10 q^{58} - 8 q^{59} - 6 q^{61} + 6 q^{62} + q^{63} + q^{64} - 4 q^{67} + 4 q^{68} + 4 q^{69} + q^{72} + 12 q^{73} - 6 q^{74} + 5 q^{75} - 6 q^{76} - 2 q^{78} + q^{81} + 12 q^{82} - 14 q^{83} - q^{84} + 8 q^{86} - 10 q^{87} + 10 q^{89} + 2 q^{91} - 4 q^{92} - 6 q^{93} + 2 q^{94} - q^{96} + 10 q^{97} + q^{98}+O(q^{100}) \) 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 0 −1.00000 1.00000 1.00000 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)
\(7\) \(-1\)
\(11\) \(-1\)

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 5082.2.a.s 1
11.b odd 2 1 462.2.a.b 1
33.d even 2 1 1386.2.a.i 1
44.c even 2 1 3696.2.a.y 1
77.b even 2 1 3234.2.a.k 1
231.h odd 2 1 9702.2.a.bt 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
462.2.a.b 1 11.b odd 2 1
1386.2.a.i 1 33.d even 2 1
3234.2.a.k 1 77.b even 2 1
3696.2.a.y 1 44.c even 2 1
5082.2.a.s 1 1.a even 1 1 trivial
9702.2.a.bt 1 231.h odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(5082))\):

\( T_{5} \) Copy content Toggle raw display
\( T_{13} - 2 \) Copy content Toggle raw display
\( T_{17} - 4 \) Copy content Toggle raw display
\( T_{19} + 6 \) 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
$13$ \( T - 2 \) Copy content Toggle raw display
$17$ \( T - 4 \) Copy content Toggle raw display
$19$ \( T + 6 \) Copy content Toggle raw display
$23$ \( T + 4 \) Copy content Toggle raw display
$29$ \( T - 10 \) Copy content Toggle raw display
$31$ \( T - 6 \) Copy content Toggle raw display
$37$ \( T + 6 \) Copy content Toggle raw display
$41$ \( T - 12 \) Copy content Toggle raw display
$43$ \( T - 8 \) Copy content Toggle raw display
$47$ \( T - 2 \) Copy content Toggle raw display
$53$ \( T - 6 \) Copy content Toggle raw display
$59$ \( T + 8 \) Copy content Toggle raw display
$61$ \( T + 6 \) Copy content Toggle raw display
$67$ \( T + 4 \) Copy content Toggle raw display
$71$ \( T \) Copy content Toggle raw display
$73$ \( T - 12 \) Copy content Toggle raw display
$79$ \( T \) Copy content Toggle raw display
$83$ \( T + 14 \) Copy content Toggle raw display
$89$ \( T - 10 \) Copy content Toggle raw display
$97$ \( T - 10 \) Copy content Toggle raw display
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