Properties

Label 5082.2.a.ba
Level $5082$
Weight $2$
Character orbit 5082.a
Self dual yes
Analytic conductor $40.580$
Analytic rank $1$
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: \(1\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} + q^{9} + q^{12} - 6 q^{13} + q^{14} + q^{16} - 4 q^{17} + q^{18} - 6 q^{19} + q^{21} - 4 q^{23} + q^{24} - 5 q^{25} - 6 q^{26} + q^{27} + q^{28} - 6 q^{29} - 2 q^{31} + q^{32} - 4 q^{34} + q^{36} + 10 q^{37} - 6 q^{38} - 6 q^{39} + 4 q^{41} + q^{42} - 8 q^{43} - 4 q^{46} - 6 q^{47} + q^{48} + q^{49} - 5 q^{50} - 4 q^{51} - 6 q^{52} - 10 q^{53} + q^{54} + q^{56} - 6 q^{57} - 6 q^{58} + 2 q^{61} - 2 q^{62} + q^{63} + q^{64} - 4 q^{67} - 4 q^{68} - 4 q^{69} + 16 q^{71} + q^{72} - 12 q^{73} + 10 q^{74} - 5 q^{75} - 6 q^{76} - 6 q^{78} + 16 q^{79} + q^{81} + 4 q^{82} + 2 q^{83} + q^{84} - 8 q^{86} - 6 q^{87} - 6 q^{89} - 6 q^{91} - 4 q^{92} - 2 q^{93} - 6 q^{94} + q^{96} - 6 q^{97} + q^{98} + O(q^{100}) \)

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

\( T_{5} \)
\( T_{13} + 6 \)
\( T_{17} + 4 \)
\( T_{19} + 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( -1 + T \)
$5$ \( T \)
$7$ \( -1 + T \)
$11$ \( T \)
$13$ \( 6 + T \)
$17$ \( 4 + T \)
$19$ \( 6 + T \)
$23$ \( 4 + T \)
$29$ \( 6 + T \)
$31$ \( 2 + T \)
$37$ \( -10 + T \)
$41$ \( -4 + T \)
$43$ \( 8 + T \)
$47$ \( 6 + T \)
$53$ \( 10 + T \)
$59$ \( T \)
$61$ \( -2 + T \)
$67$ \( 4 + T \)
$71$ \( -16 + T \)
$73$ \( 12 + T \)
$79$ \( -16 + T \)
$83$ \( -2 + T \)
$89$ \( 6 + T \)
$97$ \( 6 + T \)
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