Properties

Label 6017.2.a.b
Level 6017
Weight 2
Character orbit 6017.a
Self dual yes
Analytic conductor 48.046
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 6017 = 11 \cdot 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6017.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q + 2q^{3} - 2q^{4} + 4q^{5} + 2q^{7} + q^{9} + O(q^{10}) \) \( q + 2q^{3} - 2q^{4} + 4q^{5} + 2q^{7} + q^{9} + q^{11} - 4q^{12} + q^{13} + 8q^{15} + 4q^{16} + 8q^{17} - 5q^{19} - 8q^{20} + 4q^{21} + 6q^{23} + 11q^{25} - 4q^{27} - 4q^{28} + 5q^{29} + 10q^{31} + 2q^{33} + 8q^{35} - 2q^{36} + 2q^{39} - 10q^{43} - 2q^{44} + 4q^{45} - 9q^{47} + 8q^{48} - 3q^{49} + 16q^{51} - 2q^{52} - 10q^{53} + 4q^{55} - 10q^{57} - 14q^{59} - 16q^{60} - 14q^{61} + 2q^{63} - 8q^{64} + 4q^{65} - q^{67} - 16q^{68} + 12q^{69} + 12q^{71} - 2q^{73} + 22q^{75} + 10q^{76} + 2q^{77} + 4q^{79} + 16q^{80} - 11q^{81} + 6q^{83} - 8q^{84} + 32q^{85} + 10q^{87} - 6q^{89} + 2q^{91} - 12q^{92} + 20q^{93} - 20q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

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
0 2.00000 −2.00000 4.00000 0 2.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

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 6017.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6017.2.a.b 1 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(11\) \(-1\)
\(547\) \(1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6017))\):

\( T_{2} \)
\( T_{3} - 2 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 2 T^{2} \)
$3$ \( 1 - 2 T + 3 T^{2} \)
$5$ \( 1 - 4 T + 5 T^{2} \)
$7$ \( 1 - 2 T + 7 T^{2} \)
$11$ \( 1 - T \)
$13$ \( 1 - T + 13 T^{2} \)
$17$ \( 1 - 8 T + 17 T^{2} \)
$19$ \( 1 + 5 T + 19 T^{2} \)
$23$ \( 1 - 6 T + 23 T^{2} \)
$29$ \( 1 - 5 T + 29 T^{2} \)
$31$ \( 1 - 10 T + 31 T^{2} \)
$37$ \( 1 + 37 T^{2} \)
$41$ \( 1 + 41 T^{2} \)
$43$ \( 1 + 10 T + 43 T^{2} \)
$47$ \( 1 + 9 T + 47 T^{2} \)
$53$ \( 1 + 10 T + 53 T^{2} \)
$59$ \( 1 + 14 T + 59 T^{2} \)
$61$ \( 1 + 14 T + 61 T^{2} \)
$67$ \( 1 + T + 67 T^{2} \)
$71$ \( 1 - 12 T + 71 T^{2} \)
$73$ \( 1 + 2 T + 73 T^{2} \)
$79$ \( 1 - 4 T + 79 T^{2} \)
$83$ \( 1 - 6 T + 83 T^{2} \)
$89$ \( 1 + 6 T + 89 T^{2} \)
$97$ \( 1 + 13 T + 97 T^{2} \)
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