Properties

Label 5082.2.a.n
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

\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} + 2q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} + q^{4} + 2q^{5} - q^{6} + q^{7} - q^{8} + q^{9} - 2q^{10} + q^{12} + 2q^{13} - q^{14} + 2q^{15} + q^{16} + 2q^{17} - q^{18} + 2q^{20} + q^{21} - q^{24} - q^{25} - 2q^{26} + q^{27} + q^{28} + 2q^{29} - 2q^{30} + 4q^{31} - q^{32} - 2q^{34} + 2q^{35} + q^{36} - 2q^{37} + 2q^{39} - 2q^{40} + 10q^{41} - q^{42} - 4q^{43} + 2q^{45} + 4q^{47} + q^{48} + q^{49} + q^{50} + 2q^{51} + 2q^{52} - 2q^{53} - q^{54} - q^{56} - 2q^{58} - 12q^{59} + 2q^{60} + 2q^{61} - 4q^{62} + q^{63} + q^{64} + 4q^{65} + 12q^{67} + 2q^{68} - 2q^{70} + 8q^{71} - q^{72} - 6q^{73} + 2q^{74} - q^{75} - 2q^{78} + 8q^{79} + 2q^{80} + q^{81} - 10q^{82} + 8q^{83} + q^{84} + 4q^{85} + 4q^{86} + 2q^{87} - 14q^{89} - 2q^{90} + 2q^{91} + 4q^{93} - 4q^{94} - q^{96} - 14q^{97} - q^{98} + O(q^{100}) \)

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 1.00000 −1.00000 1.00000 −2.00000
\(n\): 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.n 1
11.b odd 2 1 462.2.a.g 1
33.d even 2 1 1386.2.a.a 1
44.c even 2 1 3696.2.a.m 1
77.b even 2 1 3234.2.a.p 1
231.h odd 2 1 9702.2.a.r 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
462.2.a.g 1 11.b odd 2 1
1386.2.a.a 1 33.d even 2 1
3234.2.a.p 1 77.b even 2 1
3696.2.a.m 1 44.c even 2 1
5082.2.a.n 1 1.a even 1 1 trivial
9702.2.a.r 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5082))\):

\( T_{5} - 2 \)
\( T_{13} - 2 \)
\( T_{17} - 2 \)
\( T_{19} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( -1 + T \)
$5$ \( -2 + T \)
$7$ \( -1 + T \)
$11$ \( T \)
$13$ \( -2 + T \)
$17$ \( -2 + T \)
$19$ \( T \)
$23$ \( T \)
$29$ \( -2 + T \)
$31$ \( -4 + T \)
$37$ \( 2 + T \)
$41$ \( -10 + T \)
$43$ \( 4 + T \)
$47$ \( -4 + T \)
$53$ \( 2 + T \)
$59$ \( 12 + T \)
$61$ \( -2 + T \)
$67$ \( -12 + T \)
$71$ \( -8 + T \)
$73$ \( 6 + T \)
$79$ \( -8 + T \)
$83$ \( -8 + T \)
$89$ \( 14 + T \)
$97$ \( 14 + T \)
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