Properties

Label 4018.2.a.g
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

\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} - 2q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} - 2q^{9} + q^{10} + q^{12} - 2q^{13} - q^{15} + q^{16} + 5q^{17} + 2q^{18} + 4q^{19} - q^{20} + 6q^{23} - q^{24} - 4q^{25} + 2q^{26} - 5q^{27} - 9q^{29} + q^{30} - 3q^{31} - q^{32} - 5q^{34} - 2q^{36} - 8q^{37} - 4q^{38} - 2q^{39} + q^{40} + q^{41} + 7q^{43} + 2q^{45} - 6q^{46} + 10q^{47} + q^{48} + 4q^{50} + 5q^{51} - 2q^{52} - 13q^{53} + 5q^{54} + 4q^{57} + 9q^{58} + 14q^{59} - q^{60} + 5q^{61} + 3q^{62} + q^{64} + 2q^{65} + 4q^{67} + 5q^{68} + 6q^{69} - 15q^{71} + 2q^{72} + 6q^{73} + 8q^{74} - 4q^{75} + 4q^{76} + 2q^{78} - 3q^{79} - q^{80} + q^{81} - q^{82} - 16q^{83} - 5q^{85} - 7q^{86} - 9q^{87} - 13q^{89} - 2q^{90} + 6q^{92} - 3q^{93} - 10q^{94} - 4q^{95} - q^{96} - 17q^{97} + O(q^{100}) \)

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 −1.00000 −1.00000 0 −1.00000 −2.00000 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.g 1
7.b odd 2 1 574.2.a.b 1
21.c even 2 1 5166.2.a.bc 1
28.d even 2 1 4592.2.a.j 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
574.2.a.b 1 7.b odd 2 1
4018.2.a.g 1 1.a even 1 1 trivial
4592.2.a.j 1 28.d even 2 1
5166.2.a.bc 1 21.c even 2 1

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4018))\):

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( 1 - T + 3 T^{2} \)
$5$ \( 1 + T + 5 T^{2} \)
$7$ 1
$11$ \( 1 + 11 T^{2} \)
$13$ \( 1 + 2 T + 13 T^{2} \)
$17$ \( 1 - 5 T + 17 T^{2} \)
$19$ \( 1 - 4 T + 19 T^{2} \)
$23$ \( 1 - 6 T + 23 T^{2} \)
$29$ \( 1 + 9 T + 29 T^{2} \)
$31$ \( 1 + 3 T + 31 T^{2} \)
$37$ \( 1 + 8 T + 37 T^{2} \)
$41$ \( 1 - T \)
$43$ \( 1 - 7 T + 43 T^{2} \)
$47$ \( 1 - 10 T + 47 T^{2} \)
$53$ \( 1 + 13 T + 53 T^{2} \)
$59$ \( 1 - 14 T + 59 T^{2} \)
$61$ \( 1 - 5 T + 61 T^{2} \)
$67$ \( 1 - 4 T + 67 T^{2} \)
$71$ \( 1 + 15 T + 71 T^{2} \)
$73$ \( 1 - 6 T + 73 T^{2} \)
$79$ \( 1 + 3 T + 79 T^{2} \)
$83$ \( 1 + 16 T + 83 T^{2} \)
$89$ \( 1 + 13 T + 89 T^{2} \)
$97$ \( 1 + 17 T + 97 T^{2} \)
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