Properties

Label 4018.2.a.k
Level 4018
Weight 2
Character orbit 4018.a
Self dual yes
Analytic conductor 32.084
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4018.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0838915322\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 574)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + 3q^{3} + q^{4} + q^{5} - 3q^{6} - q^{8} + 6q^{9} + O(q^{10}) \) \( q - q^{2} + 3q^{3} + q^{4} + q^{5} - 3q^{6} - q^{8} + 6q^{9} - q^{10} - 5q^{11} + 3q^{12} - 6q^{13} + 3q^{15} + q^{16} - 6q^{18} - q^{19} + q^{20} + 5q^{22} - 4q^{23} - 3q^{24} - 4q^{25} + 6q^{26} + 9q^{27} - 8q^{29} - 3q^{30} - 6q^{31} - q^{32} - 15q^{33} + 6q^{36} - 2q^{37} + q^{38} - 18q^{39} - q^{40} + q^{41} + 4q^{43} - 5q^{44} + 6q^{45} + 4q^{46} + 3q^{48} + 4q^{50} - 6q^{52} + 6q^{53} - 9q^{54} - 5q^{55} - 3q^{57} + 8q^{58} - 2q^{59} + 3q^{60} - 13q^{61} + 6q^{62} + q^{64} - 6q^{65} + 15q^{66} + 16q^{67} - 12q^{69} - 3q^{71} - 6q^{72} + 2q^{73} + 2q^{74} - 12q^{75} - q^{76} + 18q^{78} - 11q^{79} + q^{80} + 9q^{81} - q^{82} + 14q^{83} - 4q^{86} - 24q^{87} + 5q^{88} - 14q^{89} - 6q^{90} - 4q^{92} - 18q^{93} - q^{95} - 3q^{96} + 8q^{97} - 30q^{99} + O(q^{100}) \)

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 3.00000 1.00000 1.00000 −3.00000 0 −1.00000 6.00000 −1.00000
\(n\): 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 4018.2.a.k 1
7.b odd 2 1 4018.2.a.a 1
7.d odd 6 2 574.2.e.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
574.2.e.c 2 7.d odd 6 2
4018.2.a.a 1 7.b odd 2 1
4018.2.a.k 1 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(7\) \(-1\)
\(41\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4018))\):

\( T_{3} - 3 \)
\( T_{5} - 1 \)
\( T_{11} + 5 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( 1 - 3 T + 3 T^{2} \)
$5$ \( 1 - T + 5 T^{2} \)
$7$ 1
$11$ \( 1 + 5 T + 11 T^{2} \)
$13$ \( 1 + 6 T + 13 T^{2} \)
$17$ \( 1 + 17 T^{2} \)
$19$ \( 1 + T + 19 T^{2} \)
$23$ \( 1 + 4 T + 23 T^{2} \)
$29$ \( 1 + 8 T + 29 T^{2} \)
$31$ \( 1 + 6 T + 31 T^{2} \)
$37$ \( 1 + 2 T + 37 T^{2} \)
$41$ \( 1 - T \)
$43$ \( 1 - 4 T + 43 T^{2} \)
$47$ \( 1 + 47 T^{2} \)
$53$ \( 1 - 6 T + 53 T^{2} \)
$59$ \( 1 + 2 T + 59 T^{2} \)
$61$ \( 1 + 13 T + 61 T^{2} \)
$67$ \( 1 - 16 T + 67 T^{2} \)
$71$ \( 1 + 3 T + 71 T^{2} \)
$73$ \( 1 - 2 T + 73 T^{2} \)
$79$ \( 1 + 11 T + 79 T^{2} \)
$83$ \( 1 - 14 T + 83 T^{2} \)
$89$ \( 1 + 14 T + 89 T^{2} \)
$97$ \( 1 - 8 T + 97 T^{2} \)
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