Properties

Label 6018.2.a.j
Level 6018
Weight 2
Character orbit 6018.a
Self dual yes
Analytic conductor 48.054
Analytic rank 1
Dimension 1
CM no
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6018.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0539719364\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} - 4q^{5} + q^{6} - q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} + q^{4} - 4q^{5} + q^{6} - q^{7} + q^{8} + q^{9} - 4q^{10} - 2q^{11} + q^{12} + 2q^{13} - q^{14} - 4q^{15} + q^{16} - q^{17} + q^{18} + 7q^{19} - 4q^{20} - q^{21} - 2q^{22} - q^{23} + q^{24} + 11q^{25} + 2q^{26} + q^{27} - q^{28} - 2q^{29} - 4q^{30} + 2q^{31} + q^{32} - 2q^{33} - q^{34} + 4q^{35} + q^{36} - 2q^{37} + 7q^{38} + 2q^{39} - 4q^{40} - 7q^{41} - q^{42} - 10q^{43} - 2q^{44} - 4q^{45} - q^{46} - 6q^{47} + q^{48} - 6q^{49} + 11q^{50} - q^{51} + 2q^{52} + 3q^{53} + q^{54} + 8q^{55} - q^{56} + 7q^{57} - 2q^{58} - q^{59} - 4q^{60} - 2q^{61} + 2q^{62} - q^{63} + q^{64} - 8q^{65} - 2q^{66} - q^{68} - q^{69} + 4q^{70} - 12q^{71} + q^{72} + 7q^{73} - 2q^{74} + 11q^{75} + 7q^{76} + 2q^{77} + 2q^{78} + 16q^{79} - 4q^{80} + q^{81} - 7q^{82} - 11q^{83} - q^{84} + 4q^{85} - 10q^{86} - 2q^{87} - 2q^{88} + 9q^{89} - 4q^{90} - 2q^{91} - q^{92} + 2q^{93} - 6q^{94} - 28q^{95} + q^{96} - 17q^{97} - 6q^{98} - 2q^{99} + O(q^{100}) \)

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
1.00000 1.00000 1.00000 −4.00000 1.00000 −1.00000 1.00000 1.00000 −4.00000
\(n\): 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 6018.2.a.j 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6018.2.a.j 1 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(17\) \(1\)
\(59\) \(1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6018))\):

\( T_{5} + 4 \)
\( T_{7} + 1 \)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 - T \)
$3$ \( 1 - T \)
$5$ \( 1 + 4 T + 5 T^{2} \)
$7$ \( 1 + T + 7 T^{2} \)
$11$ \( 1 + 2 T + 11 T^{2} \)
$13$ \( 1 - 2 T + 13 T^{2} \)
$17$ \( 1 + T \)
$19$ \( 1 - 7 T + 19 T^{2} \)
$23$ \( 1 + T + 23 T^{2} \)
$29$ \( 1 + 2 T + 29 T^{2} \)
$31$ \( 1 - 2 T + 31 T^{2} \)
$37$ \( 1 + 2 T + 37 T^{2} \)
$41$ \( 1 + 7 T + 41 T^{2} \)
$43$ \( 1 + 10 T + 43 T^{2} \)
$47$ \( 1 + 6 T + 47 T^{2} \)
$53$ \( 1 - 3 T + 53 T^{2} \)
$59$ \( 1 + T \)
$61$ \( 1 + 2 T + 61 T^{2} \)
$67$ \( 1 + 67 T^{2} \)
$71$ \( 1 + 12 T + 71 T^{2} \)
$73$ \( 1 - 7 T + 73 T^{2} \)
$79$ \( 1 - 16 T + 79 T^{2} \)
$83$ \( 1 + 11 T + 83 T^{2} \)
$89$ \( 1 - 9 T + 89 T^{2} \)
$97$ \( 1 + 17 T + 97 T^{2} \)
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